La Tasca or Zizi are supposed to be good but not cheap.. Antibos for a nice italian or Le Bistoir Pierre.. For poncy...

I didn't really rate La Tasca, Zizi is ok but nothing spectacular from my past experiences. I haven't been to Le Bistoir Pierre though
Morley Hayes and Darley's are supposed to be good but haven't tried either.

Can't say there's many 'classy' places in Derby there are some nice places. Zizi and La Tasca aren't classy or nice just average mush and Antibos is full of teenage birthday parties and office nights out.
I'd suggest you look at Thai Dusit, Moonsha, The European, Anoki (as mentioned already) and Opulence (cathedral hotel) depending on what type of food you fancy.