There are lots of relatively inexpensive cheap chain hotels/motels in the city proper. The South Side and Oakland might be your best bets. There are quite a few nice hotels in Downtown Pittsburgh, but they will be a bit pricey.
Regarding getting around town, it's really best to have a car. There aren't many taxis around here. And our public transit system isn't all that great. Although, if you have to, a bus will take you where you need to go.
Things to Do:
If you want to visit a museum, there are plenty of them here. The Heinz History Center in the Strip District (focuses primarily on local and regional history); the Carnegie Museums of Art and Natural History over in Oakland (near the Pitt campus); the aforementioned Warhol Museum on the North Side; there's a Toonseum in Downtown on Liberty Avenue; finally there is the Carnegie Science Center near Heinz Field (also on the North Shore). And if you like animals, you may want to seek out the National Aviary and/or the Pittsburgh Zoo and Aquarium (the former on the Northside, the latter in Highland Park)
RE: Shopping: For records, there's Jerry's Fine Used Records over in Squirrel Hill, which is a skip, hop and a jump away from the University of Pittsburgh. For comics, there's Eide's near the Greyhound terminal, and Phantom of the Attic in Oakland. Clothing-wise, there are a lot of merchants on the South Side, in Shadyside, and in Lawrenceville. The Strip District, which is essentially a large outdoor farmer's market, is a place where you could spend hours, maybe days.
For a city its size, there's a surprisingly decent bar/restaurant scene. The South Side, specifically the area in and around East Carson St., probably has the best selection of dining options in the city. Because it's the hub of Pittsburgh's nightlife, it can get pretty hectic down there in the evenings. All in all, though, it is a fun neighborhood to visit. In addition, there are some good spots over in Lawrenceville and Garfield. And there are plenty of good, affordable restaurants in the Shadyside/Squirrel Hill/Oakland area near the universities. Of course, most everyone who visits the Burgh wants to try the infamous Primanti Bros. sandwich. I'm not all that fond of the sandwich myself, but there are others that will swear by them. The flagship Primanti's is in the Strip District on Smallman Street.
One thing I would definitely make a point of doing is visiting one of the overlooks on Mt. Washington. If you do decide to go there, make sure you go at night. You'll be rewarded with arguably the best skyline view in the entire country.
Hope this helps.
