If you have a Metro day or week pass, there is an inexpensive way to reach Mt. Vernon. Take the yellow line to its terminus, Huntington Station; exit the lower stairs; and use the Fairfax Connector bus no. 101. The cost is a mere $1 per person, and it runs about every hour. The ride (with stops) to Mt. Vernon takes about 20 minutes. This mode of arrival offers a significant advantage over the Tourmobile that departs from Arlington Cemetery.
1) You can take as much time/little time as YOU want to explore Mt. Vernon
2) There are some cost savings that can add up if your party is large. In addition, the Tourmobile service is seasonal. When ready to leave, just pick up the no. 101 right in front of the gift shop and you will be back at the Metro Station again.
Weekends are busiest at Mt. Vernon. The Saturday we were there we arrived at 10:20am (opening is 9am) and spent over a half-hour in a slow-moving line that snaked its way around the ellipse outside the mansion, through a separate building that served as servant quarters, and then inside the home. About 6,000 are said to visit on weekends per day. Mt. Vernon is not owned or operated by the National Park Service. Instead, it's an association much like the group that also owns/runs the Alamo in Texas. Upkeep of the site mandates a fee to enter therefore. Adult tickets cost $11, and children, I recall, are $8. Naturally, credit cards are accepted.
Inside the mansion, guides will offer commentary on the rooms and furnishings. Most of the furnishings are Washington's. One ingenious item we saw was a "fan chair." Given that there was, of course, no electricity, if you wanted to cool down you sat in this chair and pumped your feet on some pedals. The pedals were connected to a fan above your head. Smart. Besides the home, there are stables, carriage houses, barns with animals, and a designated kid's area that the wee ones will like. I saw kids having a blast playing with Colonial games and toys and learning something despite themselves. Do not forget to visit Washington's tomb. He lies there with Martha.
If you want to take a load off your tired feet, there are chairs on the porch facing the Potomac. The view is unchanged from Washington's day, meaning no modern development within sight to spoil the view. It’s no doubt the work of the same association that manages the mansion. There are also museums with Washington artifacts, including (although I missed them) his dentures. If you get hungry, there are fast-food merchants or a colonial-style sit-down restaurant. Time was short, so we had burgers. If you desire a souvenir, consider a flag that has flown over Mt. Vernon. They are $25, of good quality, and in the gift shop. Allow 3 hours to tour the grounds.