Peter probably means the Opera House. Do go and see that, if you can. Next door are the gardens - quite nice in summer.
Buxton also has a museum, which is vaguely interesting - lots of local finds.
If you like architecture, there is the Crescent, reminiscent of the famous crescent in Bath (forgotten its name). Buxton also has (I believe) what was at the time the widest domed roof in the UK. It's now part of Derby University.
There is Pooles Cavern on the outskirts, quite interesting.
The shops aren't very good.