Warwick is campus based, so in your first year you're sort of in a bubble with the on-site facilities. Older students tend to live in the areas around the university though, more Coventry-based I guess? Basically, you're not too far from Birmingham which has major nightlife. That said, I reckon it's easier to be somewhere where you're on top of it (i.e. a city based university, places like Manchester for instance). Being able to stumble into town on foot is handy. Check on the Warwick forums here for a more accurate view of this, that's just based off visiting it/friends there.
I personally don't like London, so I won't throw much about that. It has the most going on, and the best transport, but it's very expensive and far too busy for my liking.
I don't know too much about Bath either, but the general consensus i've seen is that there's lots of nice pubs but it'll feel rather quiet if you're used to a big city nightlife. Again, I think you're near enough to Bristol to go out there but you're not on top of it.
Have you actually thought about Manchester? As a thought it fits the nightlife, and is probably bang on for the music because there's so many gigs that go on in the city. Not sure what it's like for your course though! Leeds could be another.
Most places make the most of the nightlife around, but maybe just go check out a few of the university sub forums on here to get a feel for some other places. Lots of people have asked the question before about their specific university.