I can give you some information...as I live close to Mount Vernon:)
The George Washington Memorial Parkway (GW Parkway for short) is part of the National Park Service. Along with the GW Parkway, the Mount Vernon Trail follows along the Potomac River. This trail is used for walking, running, and biking. There are many stops along this trail...including lookouts, parks, picnic areas, etc. Here is a website that gives info about both items.
Click on "directions" and then "maps" to print out a map of the entire
GW Parkway and the Mount Vernon Trail.
There are no hotels/motels on the GW Parkway. The closest are on Route One/Richmond Highway, but I would not suggest any of these (very commercial and in my opinion, not very nice). Your next option would be Old Town Alexandria (north from Mount Vernon via the GW Parkway). This a beautiful and historic town. Here is website that will help with Alexandria information.
Possibly a bed and breakfast may work (although the price may not work and some require more than one night)...
Alexandria/Arlington bed and breakfast website: http://aabbn.com/
A b&b close to Mount Vernon (don't know anyone who has stayed here, but I know the area and house...beautiful: bedandbreakfast.com/virginia-alexandria-mt-v…
Good luck and post with more questions!