There are a few western style bars spread across Wuhan. The sheer size and scale of this city means that it is difficult to organize anything approaching a "pub crawl" but the lively atmosphere in some spots makes up for the inconvenience.
One of the busiest (and often most seedy) areas of the city is Hankou. At night especially the dodgy local Mafia types like to hang out around these parts and make their presence known! It all seems (generally) to be pretty harmless though. Brave this "experience" if you dare!
Around the University (Wuhan Da Xue) is a good area to find some smaller and more relaxed places to have a drink. The streets around Ba Lu are especially good and the Festival Bar is currently popular with foreign students in the city. A similar place is the Sunshine Bar near the Shangri La hotel. This place have live music and an entertaining "floor show".
The Primeval Forest and the long established Jo Jos are also popular hang outs. Both these places are a little more expensive than the bars around the university but they are good fun and the Primeval Forest also do good food.
Many of the hotels have decent bars too. The Shangri La has a rather up market American Sports Bar which is always popular with the ex- pat crowd and the both the Holiday Inn Hotels here also have pleasant places.