I think the rejuvenated canal area is the Brindley Place development, close to the International Congress Centre. Restaurants and the like, nice in the evenings.
Ronnie Scott's doesn't seem to have much jazz these days ... full of Birmingham's bright young things into whatever they're into.
An afternoon isn't very long. If you want to see anything, you'll really need more time, but in the best positive spirit:
1. get to Birmingham International station (close to airport) or Birmingham New Street station (city centre);
2. get on train;
3. go - anywhere!
4. get back in time for your onward flight.