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 almost as good as free, 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.
For a glimpse of old Bangkok away from most of the tourist crowds, check out Pak Klong Talad, the city's flower market, which is at its best in the wee hours of the morning, and doesn't cost a single baht, unless you want a bouquet of roses or an array of tropical plants. 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.