Badami Fort climbs the northern cliffs above Agastya Lake, where later walls and gateways share space with much older sacred structures. The remains are fragmentary, but the walk gives you the best overview of the town's geography.
Go for the views and the sense of enclosure. From the top, the cave temples, lake, Bhutanatha group, and old town snap into a single landscape, which is exactly how Badami should be read.