Here are 3 clubs I have visited here in the Pittsburgh area if your interested. None of them however, are in Pittsburgh itself, but rather in outlaying communities. Maybe a 30 to 45 minute drive from downtown Pittsburgh for all of them. Sorry, but I don’t know of any individual’s layouts available for visitors.
The Western Pennsylvania Model Railroad Museum in Gibsonia and listed in Tom’s post above is a VERY nice layout. Unfortunately, it’s only open to the public from mid-November through mid-January. Most of the open houses I know in western PA/eastern OH are in the fall.
The Science Center is located on Pittsburgh’s North Side. They do close the layout for a period of time each year, so you might want to call and see when that’s scheduled for 2013. And Tom is right about the clubs usually being opened to the public during the holidays. But contacting them might open some doors. I’m pretty sure anybody is welcome at the Beaver County club on their meeting nights.