Other than the Rameswaram Temple and Agnitheertham(Sea near the temple), other must watch places which should not be missed are
1. Pamban Bridge
From Rameswaram Temple, catch Bus No 1 which goes to Bus stand. From there you can get into bus going to mainland. Buses will be stopping at entrance of brdige, from where we can walk through road bridge. Check the NTES and plan accodingly to see the trains.
2....
more... Dhanuskodi
You can hire 4 wheel jeep or van from RMM for Dhanuskodi trip. The meeting point of Indian ocean and Bay of bengal is nice place. And the entire beach is very clean. Pure from all sort of pollution we human creates. They will take you to old dhanuskodi town as well
3. Rama Padham.(From there you can see entire Rameswaram)
You can hire auto for this. This will be part of local sight seeing