I maintain that the best way to get to know an area is to get lost in it. Being on a bike combines the flexibility of off-road paths with the speed of travel being about 5x that of walking.

Every time I move to a new city, one of the first things I do is go out with nothing but a bike, my house keys, and a little cash (just in case). Friends are still amazed I can get from one place to another so quickly without resorting to GMaps or similar.