I agree, if I was traveling, I would probably connect to the CL in Washington.
However, being a former resident of Pittsburgh, if you do make the 4-hour connection there I suggest that you leave the station and enjoy downtown. Downtown Pittsburgh is compact, easily-walkable, and safe. The subway is free downtown (but has very few stops).
I would definitely recommend walking the short distance to the Wood St. T station or Steel Plaza and riding the T across the river to Station Square. Exit the T and ask for a continuation fare for the incline. The Monongahela Incline is adjacent to the Station Square Station. You can ride it to the top of Mt. Washington and experience breathtaking views of downtown. I used to live right by the Mon Incline and I think it's one of the best views anywhere. When you've walked around and are ready to descend, ask the Incline operator for a continuation fare downtown. All together this round trip from downtown to Mt. Washington and back shouldn't cost more than about 5 bucks (depending on how much the Port Authority has raised their prices since I moved to Texas). You might also catch a cab at Station Square or the Amtrak Station and visit the waterfront casino. There are plenty of ways to pass the time, and it would be a shame to waste 4 hours in Pittsburgh's underwhelming Amtrak waiting area.
A cab or city bus could also take you from the station to the nearby Strip District. Although most of the shops will be closed, two of my favorite restaurants are there... Kaya and Eleven. There's also the famous Primanti Brothers, with fries and cole slaw on the sandwich.