Hey Anshuman,
You would need 2 to 3 days in Rameshwaram as far as the Places of interest is concerned ...
Here are few you should not miss when you travel to this beautiful peace of Southern India :-
Ramanathaswamy temple
Agni Thirtham
Gandhamadana Parvatham
Hanuman temple
Pamban bridge is a must though ...
The ghost Dhanuskodi is also worth a visit
Abdul kalam house
Bird sanctuary
don't miss to taste meen kolumbu there Bro ...
Happy Travelling Bro!!!
If you are talking about the whole trip, it would depend on from where you are starting and what mode of transport are you using. Otherwise you can finish Rameshwaram in 2 days comfortably.