He is asking about the place for Eid prayer
Question

We heard that at the time of the Prophet (peace and blessings of Allah be upon him), the Eid prayer was held in a musalla (prayer-place) outside the built-up area, because his mosque could not accommodate all the people, and that if there is a mosque that can accommodate the people, then it is better for them to pray there because the mosque is better than anywhere else. Is this correct?.
Praise be to Allah.The practical Sunnah of the Prophet (peace and blessings of Allah be upon him) (i.e., what he did) was to leave his mosque for the Eid prayers and perform these prayers in the musalla that was at the outer gate of Madeenah. See Zaad al-Ma’aad by Ibn al-Qayyim, 1/441. 
Shaykh Ahmad Shaakir (may Allah have mercy on him) said: The views of the scholars concerning that are closely connected: 
In Sharh al-Bukhaari, the Hanafi scholar al-‘Ayni discussed the following hadeeth of Abu Sa’eed [al-Khudri]: “The Messenger of Allah (peace and blessings of Allah be upon him) used to go out to the prayer-place on the day of al-Fitr and al-Adha. The first thing that he did was to pray, then he would move away and stand facing the people, when the people were (still) sitting in their rows, and he would exhort them and advise them and issue commands to them. If he wanted to dispatch an army he would do so, and if he wanted to issue some command, he would do so. Then he would leave.” Abu Sa’eed said: The people continued to do that until I came out with Marwaan when he was the governor of Madeenah, on (the day of) al-Ahda or al-Fitr. When we came to the prayer place, there was the minbar that had been built by Katheer ibn al-Salt.  Marwaan wanted to ascend the minbar; I grabbed his clothes but he pulled away, and he ascended and delivered the khutbah before the prayer. I said to him: “You have changed it, by Allah.” He said: “O Abu Sa’eed, gone is that which you know.” I said: “By Allah, what I know is better than that which I do not know.” He said: “The people will not sit and listen to us after the prayer so I did it before the prayer.” 
Narrated by al-Bukhari, 956; Muslim, 889.  
Al-‘Ayni said: This shows that we should go out to the prayer-place and not offer the Eid prayer in the mosque except in case of necessity. Ibn Ziyaad narrated that Maalik said: The Sunnah is to go out to the prayer-place except for the people of Makkah, who should pray in the mosque.
In al-Fataawa al-Hindiyyah (vol. 1, p. 118) it says: Going out to the prayer-place for Eid prayer is Sunnah, even if the Jaami’ Mosque is large enough to accommodate them. This is the view of the majority of shaykhs and it is the correct view. 
In al-Mudawwanah al-Marwiyah ‘an Maalik (vol. 1, p. 171), Maalik said: The Eid prayer should not be offered in two places, and they should not pray in their mosques, rather they should all go out as the Prophet (peace and blessings of Allah be upon him) went out. And Ibn Wahb narrated from Yoonus that Ibn Shihaab said: The Messenger of Allah (peace and blessings of Allah be upon him) used to go out to the prayer-place, then the people of the regions followed that Sunnah. 
Ibn Qudaamah al-Hanbali said in al-Mughni (vol. 2, no. 229-230): The Sunnah is to offer the Eid prayer in the prayer-place. This was enjoined by ‘Ali (may Allah be pleased with him) and was regarded as good by al-Awzaa’i and Ashaab al-Ra’i. This is also the view of Ibn al-Mundhir. 
It was narrated from al-Shaafa’i that if the mosque of a city is spacious, then it is better to pray there, because it is the best and purest place. Hence the people of Makkah pray (Eid) in al-Masjid al-Haraam. 
Then Ibn Qudamah quoted evidence to support his view, and said: Our evidence shows that the Prophet (peace and blessings of Allah be upon him) used to go out to the prayer-place and leave his mosque, as did the caliphs after him. The Prophet (peace and blessings of Allah be upon him) would not forsake the better thing even though it was closer and take the trouble to go to an imperfect place that was further away, and he did not prescribe for his ummah that they should forsake that which is good and virtuous. We have been commanded to follow the Prophet (peace and blessings of Allah be upon him) and take him as our example. It cannot be the case that the thing that is enjoined is imperfect and the thing that is forbidden is perfect. There is no report that the Prophet (peace and blessings of Allah be upon him) offered the Eid prayer in his mosque except when there was a reason or excuse. This is also the consensus of the Muslims. The people in all ages and in all places have gone out to the prayer-place and offered the Eid prayer there, regardless of whether the mosque is spacious or otherwise. The Prophet (peace and blessings of Allah be upon him) used to offer the Eid prayer in the prayer-place even though his mosque is such a venerable place. 
And I – Ahmad Shaakir is speaking – say that words of Ibn Qudaamah, “There is no report that the Prophet (peace and blessings of Allah be upon him) offered the Eid prayer in his mosque except when there was a reason or excuse”, is a reference to the hadeeth of Abu Hurayrah which is narrated by al-Haakim in al-Mustadrak (vol. 1, p. 295): “Rain fell on the day of Eid, so the Prophet (peace and blessings of Allah be upon him) prayed in the mosque.” This was classed as saheeh by him (al-Haakim) and al-Dhahabi. [And Ibn al-Qayyim said of it: If the hadeeth is proven, it is also narrated in Sunan Abi Dawood and Ibn Maajah. Zaad al-Ma’aad, 1/441. But it was classed as da’eef by al-Albaani in Risaalat Salaat al-Eidayn fi’l-Musalla hiya al-Sunnah, and he narrated the view of al-Haakim and al-Dhahabi]. 
Imam al-Shaafa’i said in al-Umm (vol. 1, p. 207): “We have heard that the Messenger of Allah (peace and blessings of Allah be upon him) used to go out on the two Eids to the prayer-place in Madeenah, as did those who came after him, and most of the people in all countries, except Makkah (concerning which) we have not heard that any of the salaf led them in offering the Eid prayer except in their mosque. I think that this – and Allah knows best – is because al-Masjid al-Haraam is the best spot on earth, so they did not like to pray anywhere else if possible. 
“If there is a town and the mosque of its people is big enough to accommodate them, I do not think that they should go out of it, but if they do go out, there is nothing wrong with that. If it is big enough and their imam leads them in prayer there, I regard that as makrooh but they do not have to repeat it. If there is an excuse such as rain etc, I would tell them to pray in the mosque and not go out to the desert.” 
The scholar Ibn al-Haaj said in al-Madkhal (vol. 2, 283): The proven Sunnah with regard to the Eid prayer is that it should be offered in the prayer-place, because the Prophet (peace and blessings of Allah be upon him) said: “A prayer offered in this mosque of mine is better than a thousand prayers offered elsewhere, except in al-Masjid al-Haraam.” (al-Bukhari, 1190; Muslim, 1394). Then despite that great virtue he (peace and blessings of Allah be upon him) went out to the prayer-place and left the mosque. This clearly indicates that the command to go out to the prayer-place for Eid prayer is confirmed, so this is the Sunnah. According to the madhhab of Maalik (may Allah have mercy on him), offering the Eid prayer in the mosque is bid’ah (an innovation), unless there is some reason why it is necessary to do that, in which case it is not bid’ah, because the Prophet (peace and blessings of Allah be upon him) did not do it and neither did any of the Rightly-Guided Caliphs after him. And the Prophet (peace and blessings of Allah be upon him) commanded the women to come out to the Eid prayer, and he told the menstruating women and women in seclusion to come out. One of them said, O Messenger of Allah, one of us does not have a jilbaab.” He (peace and blessings of Allah be upon him) said: “Let her sister lends her a jilbaab so that she may witness goodness and attend the gathering of the Muslims.” (See Saheeh al-Bukhari, 324; Saheeh Muslim, 890). 
The Prophet (peace and blessings of Allah be upon him) commanded the women to go out and he prescribed the prayer out in the open so that the symbols of Islam might be manifested.
The Prophet’s Sunnah that is narrated in the saheeh hadeeths indicates that the Prophet (peace and blessings of Allah be upon him) used to offer the Eid prayer in the desert outside the city. This is how it continued during the early days of Islam, and they did not offer the Eid prayer inside the city unless there was a reason that made it necessary to do so, such as rain. 
This is the view of the four imams and other scholars and imams – may Allah be pleased with them all. I do not know of anyone who held a different opinion, apart from the view of al-Shaafa’i (may Allah have mercy on him) who preferred that the prayer be offered in the mosque if it was big enough to hold all the people of the city. Despite that he did not see anything wrong with praying in the desert even if the mosque was big enough. And he clearly stated that he regarded it as makrooh to offer the Eid prayer in the mosque if it was not big enough to hold all the people. 
These saheeh ahaadeeth and others, and the fact that this is how they continued to do it during the early days of Islam, and the views of the scholars, all indicate that offering the Eid prayers in the mosques now is a bid’ah (innovation), even according to the view of al-Shaafa’i, because there is no one mosque in our cities that can accommodate all the people of the city where it is located. 
Moreover, this is the Sunnah, to gather all the people of the city, men, women and children, so that their hearts may turn to Allah as one and they may be united, praying behind one imam, saying “Allahu akbar” and “Laa ilaaha ill-Allah”, praying to Allah with sincerity, as if they are one, rejoicing in the blessing that Allah has bestowed upon them, so that the Eid will be a true Eid.  
The Messenger of Allah (peace and blessings of Allah be upon him) commanded the women to go out to the Eid prayer with the people, and he did not exclude anyone from that. He did not even excuse those who had nothing to wear from going out, rather he commanded them to borrow something from someone else. He even commanded those who had an excuse for not praying to go out to the prayer-place, “to witness goodness and attend the gathering of the Muslims.” 
The Prophet (peace and blessings of Allah be upon him) and the caliphs after him, and the governors whom they appointed in the various cities, used to led the people in offering the Eid prayer, then they would address them, exhorting them and teaching them things that would benefit them in their religious and worldly concerns. They would command them to give in charity in that blessed gathering, upon which descended divine mercy and blessing. 
May the Muslims follow the Sunnah of their Prophet and revive the symbols of their religion, which is the source of their pride and success. 
“O you who believe! Answer Allah (by obeying Him) and (His) Messenger when he calls you to that which will give you life” [al-Anfaal 8:24]
From his commentary on Sunan al-Tirmidhi, 2/421-424.