Hi dear

Please tell us your exam centre also so  we can answer.

My AIIMS entrance exam centre was bhopal, there we stayed at our relatives home.

You can also can stay at your relatives home or you can search for the guest house or dharmashala.

You should reach the city at 7-8.
And then you can wait near examination centre.
Select such a transportation time such that you reach 2 to 3 hours before exam.
You can ask for waiting room at examination centre to the local in charge people there.