Whether it is enjoying the green spaces that give escape from the Bangkok traffic and heat, or people watching in the fantastic traditional markets or futuristic boutique malls, you don't have to break the bank in Bangkok, nor even spend any baht for that matter. Spots like the giant green space of Bang Krachao or Suan Rot Fai come without a price tag. and centrally located Lumpini Park is a great public oasis that even has free symphony performances in the cool season!
The traditional floating market life along the Klong Bang Luang in Thonburi is fascinating, but the main reason to come here is to watch the traditional Thai puppet shows at the Baan Silapin Artist's House. Performances are free, but they do welcome donations. Chinatown is also a fantastic place for people watching and walking, there is everything from temples to market alleys to street vendors selling delicious food that is quite cheap, and make sure to take in a free Chinese opera if one happens to be going on. If the crowds are a bit much, consider heading out to Ko Kret Island, Bangkok's urban escape, where you can go bicycle riding, check out some fantastic pottery, and enjoy a bit of Mon culture, none of which cost a baht other than the bike rental fee or nominal public bus/ferry ticket to get out here.
For an afternoon of free art exhibitions, the cool Bangkok Art & Culture Centre always has something going on, and is a great local place to hang out. Finally, for something really weird, go check out the collection of buffalo skulls at the bizarre temple of Wat Hua Krabeu. There is plenty to do here for free.