Sri Lanka is a wonderful country, so definitely worth looking into.

Cochin in Kerala is also accessible (I believe Spicejet fly the route), and that's another rather special part of the world.

You can also get into Tamil Nadu quite easily. Although Chennai itself isn't a tourist destination (and has a pretty awful airport), you can quite easily get down to Pondicherry, across to the Andamans, and into the wilds of a very underrated state.