Last time I was there, you could get some sort of inexpensive day pass that was good for unlimited public transport and admittance to a long list of museums and such. However, by the time I got free, they were all closed.
I had a good time one afternoon just sitting at a sidewalk cafe near the intersection of Bahnofstrasse and Bürkliplatz, sipping a beer and watching every over-the-top ludicrously expensive sports car you've ever heard of go past. Mostly driven by middle-eastern-looking kids.
Also did some out-and-back bicycle day trips to check out the countryside. It's easy to get in and out of town following the wanderwegs. Old town and all around the lake are great for photography.