The Victoria or it’s sister the Island Bar
The (aforementioned) Wellington
The Flapper (for all your alterna-rock needs)
The Old Joint Stock for if you feel swanky (’tis a lovely place, and backs onto The Wellington)
The Old Contemptibles for similar.
Brewdog Birmingham for a hipster ale experience (I presume – it’s always so full I’ve not bothered going in).
And for a novel experience, why not try the bar inside the new library – you could then take said beers/wine/champagne out onto the roof garden!
Broad street has always been a nasty, fighty place at the best of times, but at least used to have a range of bars – the place looks like everyone’s just given up on it now. Brindley place is still okay, but I’d not bother going any further.
Maybe wander down to Digbeth or The Arcadian and go in any that you like the look of..