The Allegheny County Health Department posts listings of new food establishments on their web site each month. You can see the full list for February here, but keep in mind that it includes every establishment with a food license (e.g. GetGo). Here's a little more information on some of the openings.
Cenci’s Italian Restaurant, 11530 Perry Hwy, Pine, 724-940-5500
Cenci's Pizza Roma has offered take out for years, but just last week they opened a restaurant. They're open every day for lunch and dinner from 11 a.m. to midnight. They'll have happy hour specials Monday through Friday from 5 to 7 p.m.
E2, 5904 Bryant St, East Liberty, 412-441-1200
Enrico Biscotti's newest location in Highland Park will serve brunch on Saturday and Sunday mornings from 9 a.m. to 3 p.m. Take a look at a sample brunch menu here. They also have an event space that can accommodate up to 100 people.
PI, 1707 East Carson St, Southside, 412-431-5095
The original Pi Pizza was located in Squirrel Hill on Forbes Avenue, but it closed in 2005. I'm still awaiting confirmation on whether the new South Side spot is run by the same people (they don't seem to pick up their phone), but hopefully someone will be able to confirm that soon. According to the ACHD, they're open every day from 4 to 10:30 p.m. with a DJ Thursday through Saturday and happy hour deals Monday through Friday from 4 to 6 p.m.