I lived in Bangkok for two years. The most conventional things I did while there were Ayyuthaya (the buddha head in the roots of the bodhi tree), Hua Hin (beach town), Kanchanaburi (Bridge on the River Kwai), and Koh Samet (an island). That said:

I went to Ayyuthaya on the local train, which was more interesting than the destination. Same for Hua Hin, where I stayed in a little low-key hotel and I walked to and out on a nearly-abandoned pier. Same for Kanchanaburi where I got off a stop early and had to pay a local to drive me to the final stop, and I stayed in a low-key floating hotel in a fan room. I took a bus (and a boat) to Koh Samet and walked from one end of the island road to the other, and got to watch people playing Takraw at the police station.

Wandering is a great way to see a place.