Regent Square is right off the Parkway East, between Swissvale and Wilkinsburg. To get to Regent Square from Oakland, take Forbes Avenue through Squirrel Hill until you get to Braddock Avenue. Nice neighborhood shopping area, complete with bakery and movie theater. Shadyside is a 15 or 20 minute walk from Oakland up Fifth Avenue. This is a very convenient place to live.
Rich families live here as well as yuppies, artists, and students.
Walnut Street is a great place to shop or just people-watch. Unfortunately, rents can be rather high, and break-ins sometimes a problem. South Side is a short ride away from Oakland on PAT's 54C, which comes every 20 minutes via 18th Street. Rents have increased too, in the flats, but decent deals are still available. Squirrel Hill is about as close as Shadyside to the University and also can be reached by shuttle.