Hi Divya, it's so beautiful that you are traveling with your grandparents. You have two options, either start in Tirupati and go south or start in Rameshwaram and move up. Tirupati itself has an airport that you can fly to. Or, you can fly to Chennai Airport (150km) and hail a taxi to Tirupati. The closest airport to Rameshwaram is Madurai Airport (149km). You can hire a taxi from Madurai to Rameshwaram. Since you are traveling with your grandparents, I suggest that you take a flight from Tirupati/Chennai to Madurai or vice versa. Because, by road it's a 12 hour journey. As for places to visit goes, do check out Meenaxi Temple (Madurai), Dhanushkodi, Thanjavur, Pichavaram Mangroves and Pondicherry. I am attaching an article. Yes, it is titled Backpacking Trail but you will get an idea of the places mentioned.
It will be nearer from madhurai airport to Rameshwaram, if you want to avoid road trip from chennai. The main place you should not miss is Dhanushkodi. It is 7km from Rameshwaram and the gates will open only from morning 6am to evening 6pm.