The exhibit is still at the Children's museum -
https://pittsburghkids.org/exhibits/fred-rogers-us
I don't see anything recent, but this past November the station where he did his shows (WQED) had tours of the set.
https://pittsburghkids.org/exhibits/fred-rogers-us. It couldn't hurt anything to call the station and ask if there are plans to do more tours or what they would suggest.
I've never been there, but on the way to Pittsburgh (about 45 minutes or so outside the City) is an amusement park geared towards kid (think Dutch Wonderland). They had one section devoted to Mr. Rogers but I don't see anything about it now - it may have been replaced with Daniel Tiger Stuff. Call and find out.
http://www.idlewild.com/things-to-do/park-map
Last but not least, stop by the Manor Theater in Squirrel Hill to watch a movie. I'll never forget the time I saw a movie there and who walks in but Mr. and Mrs. Rogers! Talk about really being in Mr. Rogers's neighborhood.