I'm not sure your specific schedule, but here are a few things to consider...
Your schedule will not probably not work, but this company's bike tours take you off the beaten path through neighborhoods and farms and such you'd never see on your own. These people are so cool. You'll learn a lot about culture, etc. as well.
Go see some temples. I think they close fairly early, but they are worth seeing even from the outside. You can take the river "taxi/bus". Don't hire the private boat or a tour. If you do plan to go in, wear pants. If you don't have pants, the larger temples will have scrubs for you to wear. (note for SE Asia travel... men wear pants. Only white dudes and children wear shorts. This is slowly changing, but I figured I'd give some old fashion, grumpy old man, backroom sartorial advice.)
Get a legit massage. Health Land is recommended by my local friends (maybe because it is near our company preferred hotel).
Muay Thai. There is a white person entrance with high entrance fees. You can also show up in person (via taxi) and talk them into the local entrance. (you will be rejected several times before they relent) The local seating is way more fun because they are wagering on all of the matches. An easy way to get in to the local area is finding a local looking guy and explaining you want to join the local guys gambling. Thai culture is a bit modest, so don't go in there showing off your "big swinging dick." This aint Vegas. Be curious and enthusiastic, and you'll get in. Thai people are extremely friendly.
Walk around Nana Plaza. Nana Plaza is one of the two red light districts in the Sukhumvit area. (other is Soi Cowboy) It is interesting to walk around and see all the street vendors selling grilled bugs and other street foods. Lots of lady boys walking around. Later at night, you will likely find a Thai version of craps being played. Once again, by being modest, curious, and enthusiastic, they will let you in the game.