RedCoffee, to echo
islandboi8204 and
ForkAndSpoonOperator, Philly Tap Finder can be a great asset. It's usually accurate and there are a ton of bars listed on it. As for West Philly/University City, Local 44 is by far the best option. It's at 44th and Spruce and an easy walk from anywhere in U. City. They've always got a pretty good draft list and are one of the better bottle shops in the city. (Despite popular legend, you can buy single bottles/six packs/12 packs in Pennsylvania. The only retailers who sell singles/sixers/12s though must also sell food (usually a deli, convenient store, etc.). But it is extremely easy to find bottle shops and Philly has a lot of good ones. But some are definitely on the pricey side, as
ForkAndSpoonOperator mentioned). Other than Local 44, City Tap House often has a great draft list, but the place kind of sucks (douchey/****** atmosphere). It's probably worth checking out though if the draft list is good (check Tap Finder). Also, Dock Street is in West Philly and definitely worth a stop. They also make some good pizza. Finally, Fiume is an awesome awesome dive bar that's above an Ethopian restaurant a block away from Local 44. They have great cocktails, despite what the aesthetic may suggest. And their whiskey list was pretty good last time I was there.
Aside from what's listed above, U City is probably the worst spot in the city for beer, so I wouldn't hesitate to seek out other neighborhoods if you have time. There are a lot of good bars just a short cab ride away in the Graduate Hospital area, (which is just over the South Street Bridge from University City) and Center City. Most of these bars are also very easy to walk to. Anywhere else in the city really isn't far by cab and cabs are fairly cheap. Also, there are a bunch of bus lines that cross the various bridges into and out of U City every few minutes (just google the routes). The bus is highly reliable and cheap.
As for local/regional drafts, I've been liking a lot of what Spring House has been doing. Their Big Gruesome is worth checking out of you see it. I love Flying Fish Exit 16 Wild Rice DIPA. You should be able to find that one on draft very easily. Carton Boat beer is a must try and will be easy to find. Bull Frog has been producing some great stuff and you should be able to find their offerings pretty easily. Their sours have been really nice and their Edgar IPA is delicious. Forest and Main usually has some taps floating throughout the city. Drink these if you see them. Neshamany Creek is a newish local brewery that makes a great pilsner, and some other nice lagers (I haven't enjoyed their ales). Free Will makes some nice stuff, but I'd rank them below the ones I've listed. If you are looking to drink strictly local, Sly Fox, Troegs and Yards will be close to ubiquitous, even at the shittiest options (same goes for Victory, but I suspect you see a lot of their stuff in Chicagoland).