The lace market area is where a lot of the better bars and pubs are. Less pikey (although there is generally a fair share of "pike" in Nottingham) than the bars directly abutting Old Market Square which are the usual hell holes likes Yate's. The Pitcher & Piano is worth a quick visit, if only for the impressive building (although maybe not the best bet for clunge and it aint cheap). I can't remember the names of too many other places but if you have a stroll round there you find something to suit your needs!
In terms of late-bars/clubs, lace market has some independent type places ranging from the alternative to the mainstream; there is a big Oceana near the middle of town (5 mins walk from Old Market Square); another "disco-ey" club called Ocean (or it used to be - not been to Notts for a few years) down near the castle - this is a popular student haunt so could be busy with young, nubile, tight, smooth clunge given that it's Halloween. There used to be a bar up the hill from Ocean called BZR which did triples for the price of singles.
Basically, everything is pretty well clustered around the centre and close together.