I've visited Pittsburgh as a tourist about every other year for most of my life. And nearly every trip includes a ride up the Mon. It remains just as fun (and a little bit scary) as when I was a kid.
Few cities boast a view like the downtown Pittsburgh skyline as seen from Mt. Washington. Bring your camera.
I recommend the Monongahela incline over the Duquesne incline because it is convenient to Station Square and a "T" station. However, once you're on top of the hill, take a walk over to the Duquesne station. It's about a mile away with some seriously graded hills, but you'll be walking along the skyline and next to some impressive hilltop homes. At the Duquesne station you'll find all sorts of historical exhibits and a gift shop. The outdoor platform might be the best view on the entire hill.
Bathrooms are not convenient at the top of Mt. Washington, so make a stop at Station Square before you head up. Also, I always travel to Pittsburgh with lots of quarters and one dollar bills. The inclines and the "T" require exact change.