I live near Wolverhampton, but don't go to the uni. The nightlife is okay, fair few bars and pubs, Indi bar is good, Walkabout is okay, not really my scene though. Not much in the way of decent nightclubs though imo. Oceana used to be okay a good few years back, but went a bit crap and now it's shut down. I always go to Birmingham, it's a million times better, taxi fare will probably be too much for you as a student though to go regularly, as you're looking at 20-40 quid each way depending on drop offs, taxi firms etc.
I know Wolves uni does these bar crawls around town called Boom, they are supposed be really good, got a few friends who love them, but I've never been on one.
Walsall is pretty rubbish, mind you I used to love it when I was underage and just turned 18, my younger brother and his mates really like it as well. It seems to attract 17-19 year olds mainly because it's cheap and the music in WS1 is fairly decent depending on what you like. But it can be quite rough. Never been to Stourbridge, but I've not heard anything about it's nightlife (make of that what you will). Same goes for Worcester, both are likely to be too far for you to afford in taxi fare as well.
To sum up, I think you're best off sticking to Wolves , the nightlife is good enough for your average student, but it's not amazing. Birmingham is a lot better, but probably too far for you to go to regularly.