Why not right outside your door?
As to the Katy and the GAP, see my signature line below. The Katy is a great ride. I would suggest something similar to what I did and start in St. Charles with a train ride to Warrensburg. I haven't got to the GAP yet in my other journal...it's coming

...but I would definitely not suggest doing a one-way trip starting in Pittsburgh. That's about 110 miles of grinding up hill. Better to start in Cumberland (or in DC if you are going to do the C&O).
I would also suggest the Elroy Sparta. Start in Grand Rapids, take the ferry across to Milwaukee, ride to Sparta via the Glacial Drumlin and Madison, then wander back via Appleton and Manitowac. That's almost 700 miles.