Glad to hear you're thinking about moving to the 'Burgh!! DH and I have both lived here our whole lives and don't plan on leaving.

Currently we live in Mt. Lebanon. It's a very nice neighborhood right by Beechview and we live within spitting distance to the T. We don't have neighbors across the street, we just have the T rails. It's great for commuting!! Plus you can ride into town and catch a bus nearly anywhere from there.
I grew up in the North Hills, but since you don't drive, that might not be the best for you. It's a great area, but the transportation isn't so great.
As for sight seeing definately check out Kennywood if you like amusement parks, Sandcastle for a waterpark, any of the museums (we have a ton) - the Carnegie Science Center is very cool, walk around the Strip District in the morning - preferably a Saturday - it's a big market place, not anything naughty.

They have a ducky tour that takes you on a tour of the city by land and water that is supposed to be pretty cool, the South Side has some really neat shops and the new South Side Works is a great place to visit, ride the incline up to Mt. Washington for a great view of the city, catch a Pirate game - general admission is only $9 and most people around here go to hang out at the stadium due to the Pirates abismal record... wow, I'm sure there's a lot more that I'm leaving out!!
There are bunches of hotels in the city, but I think they're all more expensive... it's worth checking in to though. That way you can catch a bus anywhere.
PM me if you ever have any more questions! Good luck!
