Is It Better for a Woman to Pray at Home?
Question

What is the ruling on sisters making Salah in public?
Praise be to Allah.Is it better for a woman to pray at home?
ِA woman should be protected and concealed from men as much as her guardian can do that. The Messenger (peace and blessings of Allah be upon him) preferred for women to pray in their houses and said that their reward for doing so is greater than their reward for praying in the mosque . 
It was narrated from `Abdullah ibn Mas`ud (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “A woman's prayer in her room is better than her prayer in her courtyard, and her prayer in her cabinet is better than her prayer in her room.” (Narrated by Abu Dawud, 570; At-Tirmidhi, 1173. This Hadith was classed as authentic by Al-Albani in Sahih At-Targhib wat Tarhib, 1/136). 
“Her room” refers to a woman`s own room in the house, and “her courtyard” refers to the central area (in a traditional Arabic house), off which all the rooms of the house open. 
A cabinet is like a small room inside the large room, in which personal items are stored. (Commentary from `Awn Al-Ma`bud). 
It was narrated that Umm Humayd (may Allah be pleased with her) the wife of Abu Humayd As-Sa`idi (may Allah be pleased with him) came to the Prophet (peace and blessings of Allah be upon him) and said, “O Messenger of Allah, I like to pray with you.” He said, “I know that you like to pray with me, but your prayer in your room is better for you than your prayer in your courtyard and your prayer in your courtyard is better for you than your praying in your house, and your prayer in your house is better for you than your prayer in the mosque of your people, and your prayer in the mosque of your people is better for you than your prayer in my mosque.” So she issued orders that a prayer-place be prepared for her in the furthest and darkest part of her house, and she used to pray there until she met Allah (i.e., died).” (Narrated by Ahmad, 26550)
This Hadith was classed as authentic by Ibn Khuzaymah in his Sahih, 3/95; Ibn Majah, 5/595; Al-Albani in Sahih At-Targhib wat Tarhib, 1/135 
It was narrated that `Aishah (may Allah be pleased with her) said: “If the Messenger of Allah (peace and blessings of Allah be upon him) had lived to see how women have started to behave, he would have prevented them [from going to the mosque] as the women of the Children of Israel were prevented.” I said, to `Umrah, “Were they prevented?” He said, “Yes.”  (Al-Bukhari, 831; Muslim, 445) 
`Abd Al-`Adhim Abadi (may Allah have mercy on him) said: 
“The reason why their praying in their homes is better is because it is safer from temptation. This was later borne out by the way in which women began to make a wanton display of their adornments, hence `A`ishah said what she said.” (`Awn Al-Ma`bud, 2/193) 
Can women pray in public places?
Hence women should be careful when praying in public places, or go far away from where men can see them , and should not pray in a public place when the time of prayer comes, unless she has no other place in which to pray.  
Shaykh `Abullah Al-Jibrin (may Allah have mercy on him) said: 
“With regard to women, their houses are better for them. If they need to pray in the marketplace and there is a place that is screened off , there is nothing wrong with them praying there, in sha Allah.” (Fatawa Al-Mar`ah Al-Muslimah, 1/333) 
But what some of the common people say, that a woman`s prayer is invalidated just because a man happens to see her, has no basis in Shari`ah at all. Women used to pray at the time of the Prophet (peace and blessings of Allah be upon him) in one mosque and he (peace and blessings of Allah be upon him) did not rule their prayer to be invalid. 
And Allah knows best.