The Exile Waiting — Vonda N. McIntyre

Center, sole surviving city in a storm-torn Earth, is like some hilltop city of the Renaissance, only wholly underground, and quarried out of a limestone cave system. The ruler is a Medici figure gone to seed: it's a hierarchical, free enterprise society and the whole place fairly hums with life. The ruler and his court of perverts try to corrupt unwelcome guests, but the heroine, a remarkably believably girl, telepath and cat-burglar to boot, manages to sort them all out and escape. (Daily Telegraph, quoted on the back jacket in lieu of description.)