Economy hotels, good luck. Your best bet on hotels in the DC area is to pick one in a suburb that is readily accessible to the Metro system. In Maryland, this might be in Bethesda, Rockville, or Silver Spring. In Virginia this might be somewhere like Alexandria or Ballston.
As for Great Falls. That area is spectacular, though not huge. Most people are amazed that its natural splendor is only a few miles from the center of the city. The most scenic views of the falls are typically seen from the Virginia side. The more extensive park that surrounds the C&O canal is on the Maryland side. I would think you could spend a few hours on the VA side, preferably in early morning. The Maryland side has more extensive trails, particularly the Billy Goat Trail that leaves from the main Great Falls park.
If Landscape is your thing, some other places to visit in the area are Harpers Ferry, West Virginia (about 75 minutes from the city) where there is a beautiful Civil War era historical town at the confluence of the Shenandoah and Potomac rivers. Above the town, in Maryland, is Maryland Heights with great views to of the river and town. Catoctin National park in Maryland is quite scenic with great rocky views. The park also contains the presidential retreat Camp David. And finally, there is Shenandoah National Park that is about two hours from the city. Lots of great scenery and hiking there.