Aisha reported: Umm Habiba and Umm Salama made a mention before the Messenger of Allah (SallAllah-u-Alaihi-wa-Sallam) of a church which they had seen in Abyssinia and which had pictures in it. The Messenger of Allah (SallAllah-u-Alaihi-wa-Sallam) said: When a pious person amongst them dies they build a place of worship on his grave, and then decorate it with such pictures. They would be the worst of creatures on the Day of judgment in the sight of Allah.
[Sahih Muslim: Book 004, Number 1076]

Aisha and Abdullah reported: As the Messenger of Allah (SallAllah-u-Alaihi-wa-Sallam) was about to breathe his last, he drew his sheet upon his face and when he felt uneasy, he uncovered his face and said in that very state: Let there be curse upon the Jews and the Christians that they have taken the graves of their Prophets as places of worship. He in fact warned (his men) against what they (the Jews and the Christians) did.
[Sahih Muslim: Book 004, Number 1082]

Ibn ‘Umar reported Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) as saying: Observe some of your prayers in your houses and do not make them graves.
[Sahih Muslim: Book 004, Number 1703]

Abu’l-Hayyaj al-Asadi told that ‘Ali (b. Abu Talib) said to him: Should I not send you on the same mission as Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) sent me? Do not leave an image without obliterating it, or a high grave without leveling it. This hadith has been reported by Habib with the same chain of transmitters and he said: (Do not leave) a picture without obliterating it.
[Sahih Muslim: Book 004, Number 2115]

Jabir said: Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) forbade that the graves should be plastered or they be used as sitting places (for the people), or a building should be built over them.
[Sahih Muslim: Book 004, Number 2116]

Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) as saying: Do not sit on the graves and do not pray facing towards them.
[Sahih Muslim: Book 004, Number 2121]

We can summarize the above hadiths as:

1. Graves are not meant to be places of worship.
2. Places for worship shouldn’t be made on any grave, no matter how pious that person might be.
3. High graves should be leveled.
4. We should observe salat at home and do not make our homes like graves meaning there is no salat at graves so don’t do the same for your home.
5. Graves shouldn’t be plastered.
6. We shouldn’t pray salat facing the graves.

Note: There are narrations in which Prophet Muhammad (SallAllah-u-Alaihi-wa-Sallam) prayed salat over a grave facing it with his companions.

Either that action was done before he forbade from doing so or that it was allowed for him as a special case as his salat benefited the dead.

Prophet Muhammad (SallAllah-u-Alaihi-wa-Sallam) said: Verily, these graves are full of darkness for their dwellers. Verily, the Mighty and Glorious Allah illuminates them for their occupants by reason of my salat over them
[Sahih Muslim: Book 004, Number 2088]

Please remember this hadith as well.

Prophet Muhammad (SallAllah-u-Alaihi-wa-Sallam) said: One should travel only for visiting three Masaajid: Masjid-ul-Haram, Masjid-ul-Aqsa, and this (my) Masjid.
[Sahih Bukhari: Volume 3, Book 31, Number 215]

If travelling for religious sites then we are restricted to three.