Avoid Balsall Heath, I lived there and it was awful. Felt scared to walk out the house sometimes.
In terms of guitar shops, theres PMT which is great if you know what you want, but there isn't a lot of selection. There was Sound Control, not sure how long that will be there, or if its still there (I left Brum two years ago you see).
Fairdeal Music is there too, not far from the Bullring, not an amazing place, but has some decent gear, always worth a look at the pedal cabinet if nothing else.
I think theres one called Musicstop on Snow Hill too, near where Sound Control is. Its a weird place, can order in most things, but not a great selection in store. One or two low end Engls, a H&K or two and a THD Flexi 50 last time I was there. Worth a look to pass the time if nothing else, and probably the most talkative and nicest staff in the area, the rest in all the other stores seem to be either jaded or on commission.