I live downtown Halifax directly across from Alexander Keith's brewery.
As far as stuff to do goes...bars bars bars!
The main strip of them is down Argyle street (and up each way of Prince st.)
But really, there's a fun bar on every block, so just explore.
Some of my favs are:
The Split Crow (go on a thursday night)
Toothy Moose and Foggy Goggle (both on Argyle)
Tribeca on Granville st. is a cool indie/dance venue.
There are usually a TON of shows playing (just check the local paper/flyers). Really good bands stop by.
Spring Garden Road (run into town perpendicular to downtown) is full of good food/shops etc. It's cool to walk down (you'll see my architecture school too!). If you're staying at the main Dal campus you'll have to walk down this road anyways to get downtown.
Everything is so close that it's super easy to explore by foot/bus.
I'd suggest taking a guided tour (tacky, I know...but there's some really cool history here and they lay it all out for you). Harbor Hopper is cool because you ride on these big amphibious military trucks (driving/boating tours)
Besides just exploring the shit out of the city (the entire metro peninsula is fairly small), that's about all I can suggest.
And remember kids, play safe.