I don't know what clubs are on, as I don't live in Edinburgh anymore.
To be honest with you, apart from the street party it's really just going to busy pubs. You're probably best off going to the Grassmarket as there are loads of pubs and the atmosphere will be good. It's also just under the castle so you'll probably hear a bit of the bands.
Edinburgh isn't that great for clubs though, although I'd check what's on at the Honeycomb and the Liquid Rooms as these are probably the best two.