Visit Trivandrum, Kovalam and Poovar. That's the best practical itinerary you can have. Enjoy at cleanest beaches of Kovalam, Take backwater ride at Poovar and Visit Sree Padmanabhaswamy Temple at Trivandrum. Also Kovalam and Poovar are quiet close to Trivandrum and easily accessible by cabs. Boat ride at Poovar can be booked online in advance at discounted rates.
If you decide to go to the waterfalls, below are must visit: Athirappilly falls
Vazhachala falls If you decide to go to Alleppey:
Mannarasala Nagaraja Temple
Visit Toddy shops I suggest since you have only 2 days, Alleppey backwaters is the place.