There are many places to visit in Trivandrum. Kerala is known for it's beautiful beaches and temples. I would suggest to visit * Padmanabhaswamy Temple,there you can witness Kerala culture.
*kovalam beach (30mins).
*poovar, once you reach there you have to take boat to reach golden sand beach which is awesome but the journey till there is itself more pretty, that's why backwaters are attraction in Kerala.
if you can travel for up to few hours then
*alleppey - try to go in evening so you can get to spend night in boathouse
*munnar - this is quite far from trivandrum but worth going I hope you'll get to visit at least few of them.