My number one thing to do is to go watch an intense football match (soccer). I'm Canadian and I've never seen or heard of such fans. The atmosphere is great. As you walk into the stadium you feel like a player stepping onto the field, it's that loud.
Second, nightlife is a wonderful venue for young adults. Go to a pub have a few drinks or go to Dave and Busters. It's a pub/mini-casino/arcade. Then go out to one of the many pumpin clubs. Whether you like dance, hip hop, or jazz, they have it all.
And my last recommendation is get a bite at a local fish and chips shop and buy a balti. Wonderful!!! or as they say Lovely!
Quick Tips:
Watch yourself at night. It can be a dangerous place. In my opinion worse than New jersey and safer than Detroit. Don't wear soccer or football shirts. I'm sorry but especially you Italians. Some of the Birmingham/England hardcores just won't appreciate it. Mugging is a possiblility so make sure you tuck some money in your socks.
Best Way To Get Around:
Best way to get around you ask?
Two words 'DOUBLE DECKER.'
England is known for them. They are simply everywhere and will get you to wherever you want.