A few years back when I visited Rameshwaram, we stayed at Hotel Tamilnadu. It is TTDC govt hotel and well maintained and the ocean view rooms are very good. You can check this hotel
Hi Mayuri:
Here are some good hotels in Rameshwaram, Madurai, and Kanyakumari:
Rameshwaram: Hotel Ashoka, Hotel Sangam, Hotel Rameshwaram Grand
Madurai: The Gateway Hotel Pasumalai, Fortune Pandiyan Hotel, Heritage Madurai by Fortune
Kanyakumari: Sparsa Resort, The Gopinivas Grand, Hotel Seaview