He does not pray in the Prophet’s Mosque so that he can pray behind an imam who he thinks helps him to have better khushoo‘ (focus) in his prayer
Question

                We were staying close to the Prophet’s Mosque in Madinah during the last ten nights of last Ramadan. One of the young men used to pray all the obligatory prayers in the Haram except for ‘Isha’ prayer, Taraweeh and qiyaam, which he prayed elsewhere on the basis that he could not focus on the prayer or feel at ease because of the voice of one of the imams of the Haram. He says that he did not want to waste the last ten nights of Ramadan, and the most important thing to him was his spirituality. One of those who were observing i‘tikaaf said: “I am observing i‘tikaaf for all of the day, except at the time of ‘Isha’ and qiyaam, which I pray outside the Prophet’s Mosque.” What do you think, may Allah preserve you?
Praise be to Allah.
      Prayers offered in the Prophet’s Mosque bring a greatly 
      multiplied reward. 

    Al-Bukhaari (1190) and Muslim (1394) narrated from Abu 
    Hurayrah (may Allah be pleased with him) that the Prophet (blessings and 
    peace of Allah be upon him) said: “One prayer in this mosque of mine is 
    better than a thousand prayers anywhere else, except al-Masjid al-Haraam.” 

    This hadeeth includes both obligatory prayers and naafil 
    prayers that it is mustahabb (recommended) to offer in congregation in the 
    mosques, such as Taraweeh. 

    The scholars of the Standing Committee for Issuing Fatwas 
    said: 

    It is mustahabb to offer naafil prayers at home, whether they 
    are regular Sunnah prayers (ar-rawaatib) or otherwise, except those 
    which Allah has prescribed should be offered in the mosque, such as the two 
    rak‘ahs offered when entering the mosque (tahiyyat al-masjid or 
    greeting the mosque); those which Allah has prescribed should be offered in 
    congregation, such as Taraweeh and the eclipse prayer, which should be 
    offered in the mosque; and Eid prayers and prayers for rain (istisqa’), 
    which should be offered in the musalla (prayer place).

    End quote from Fataawa al-Lajnah ad-Daa’imah, 7/239 

    With regard to your companion not praying Taraweeh in the 
    Prophet’s Mosque for the reasons you mentioned, undoubtedly khushoo‘ (proper 
    focus) in prayer and presence of mind in prayer is something to be sought, 
    and a beautiful voice in recitation of the Qur’an helps with that and has an 
    impact on the listener. If your companion was going to pray in another 
    mosque and that would help him to have better focus, then there is no blame 
    on him. He may have forsaken the virtue of the place and been keen to attain 
    a virtue that has to do with the prayer itself, namely khushoo‘. If there is 
    a conflict between two virtues – as is the case with your companion – then 
    precedence should be given to the virtue that has to do with the act of 
    worship itself. 

    Shaykh Ibn Jibreen said: 

    A beautiful voice and good recitation have an impact on the 
    heart and help to bring about presence of mind and physical stillness, and 
    enable one to be affected by the words of Allah, may He be exalted, and to 
    enjoy listening to them, which may be a means of understanding them, 
    comprehending their meaning and appreciating their miraculous nature, 
    eloquence and style. All of that is in turn leads acting upon them and 
    accepting their guidance. So the one who looks for a reciter with a 
    beautiful voice who recites the Qur’an well, has memorised it, whose 
    recitation helps him to focus and is unhurried in his prayer is not to be 
    criticized. One should look for such an imam to pray behind, even if the 
    place is far away, and this imam is to be preferred over one who does not 
    recite well, or makes many mistakes, or does not have a pleasant voice, or 
    does not make his voice beautiful when reciting Qur’an, or who recites too 
    quickly, or is not unhurried in his prayer, or does not sound focused in his 
    recitation, even if his mosque is nearby. End quote. 

    Fataawa ash-Shaykh Ibn Jibreen, 
    24/28 

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

    The questioner asked whether it is better to observe i‘tikaaf 
    in al-Masjid al-Haraam or elsewhere. 

    The answer is: Yes, observing i‘tikaaf in al-Masjid al-Haraam 
    is better than observing i‘tikaaf in other mosques. The next best is 
    observing i‘tikaaf in the Prophet’s Mosque, then doing so in al-Masjid 
    al-Aqsa, then other mosques, the next best then the next best. 

    But here there is an issue that we should highlight, which is 
    that paying attention to the act of worship itself is more important than 
    paying attention to its time and place. In other words, the virtues 
    pertaining to the act of worship itself are more important than the virtues 
    pertaining to its time or place. That is, if a person’s i‘tikaaf in a mosque 
    other than the three mosques will be more perfect, with a stronger focus on 
    humility before Allah, may He be glorified and exalted, in his worship, then 
    observing i‘tikaaf in those mosques is preferable, because this advantage 
    has to do with the act of worship itself. 

    The scholars think that being able to walk rapidly (raml) 
    in tawaaf al-qudoom (tawaaf of arrival, in the first three circuits) is more 
    important than getting close to the Ka‘bah. They explained that by noting 
    that walking at a rapid pace is a virtue that has to do with the act of 
    worship itself, whereas getting close to the Ka‘bah is a virtue that has to 
    do with the place; paying attention to matters that have to do with the act 
    of worship itself is more important than that which has to do with the 
    place. This is a point which people, especially seekers of knowledge, should 
    pay attention to, namely focusing on the virtue of the act of worship itself 
    more than focusing on the place or time. End quote. 

    Fataawa Noor ‘ala ad-Darb, 
    205/4-5 

    The shaykh also said: 

    Undoubtedly i‘tikaaf observed in one of the three mosques to 
    which journeys may be made is better, and there is no difference of 
    scholarly opinion on this point, except if observing i ‘tikaaf in his own 
    mosque will lead to greater khushoo‘ and focus of mind, and he will be safe 
    from noise and disturbance, and seeing inappropriate scenes. In that case, 
    we say that his own mosque is preferable. End quote. 

    Sharh al-Kaafi, 4/159 

    What appears to us to be the case is that there is nothing 
    wrong with what your companion did, even though the imams of the Haramayn 
    are carefully selected from among those who recite well and have pleasant 
    voices. 

    With regard to one of those who are observing i‘tikaaf going 
    out to pray ‘Isha’ and qiyaam outside of the Prophet’s Mosque, his i‘tikaaf 
    is not valid, because he has gone out of the mosque unnecessarily. 

    What he should do is either observe i‘tikaaf for all of the 
    last ten days in the Prophet’s Mosque, and not go out except in the case of 
    necessity, which is best; 

    Or he should observe i‘tikaaf in the mosque where he is going 
    to pray, so that he will attain the reward of observing i‘tikaaf in the last 
    ten days, and thus he will have followed the example of the Prophet 
    (blessings and peace of Allah be upon him). 

    And Allah knows best.