Badami Shivalaya refers to the early stone temples in the fort area above the lake. The Upper Shivalaya is the standout, partly ruined but beautifully placed on the ridge, where its weathered sandstone seems to grow out of the hill.
It is worth the climb even if you are not studying temple architecture. The shrine gives Badami a vertical dimension: caves below, lake in the middle, and sacred stonework watching from the ridge.