If you have a week or more to spare you could take a boat on the Kerala Backwaters from Alleppey, visit the Periyar Wildlife and Tiger Sanctuary and see the tea plantations at Munnar in the mountains, as well as spending time in the old colonial city of Fort Cochin and visiting the modern port at Ernakulam, Kochi. All of this is possible by public transport, but the quicker and more pleasant way is to hire a car and a driver, which you can do when you get here.
If you like the beach and the sea you may decide just to chill out in Kovalam, or visit Kerala’s other well-know seaside resort, Varkala.