You can park in the Mailbox car park, which is just at the back of Broad street, but as someone said, brum is a bugger to drive around if you don't know the place well. There ARE car parks all over the place, but I imagine the prices are ridiculous.
Doesn't the jury's have a customer car park?
The Bullring has a couple of cafe's in the middle that probably sell booze. Del'Villagio springs to mind. You can also get all manner of expensive drinks in Selfridges, if you want to drink in a dept store with people pushing past you all the time. broad Street is the drinking part of brum, but I'd head for the Chinese Quarter and a place called the Arcadian. Lots of bars there and it's much nicer than Broad Street.
Just out of the Bullring on New Street there's a hotel with a bar in the basement called Bacchus, which is really gothic inside and quite smart - but will be packed from about lunchtime today!
Have fun. It's a good place to go if you know where you're going.