Hm, parking at a Metro station depends on the timing of your trip. Are you planning for a weekday or weekend venture into DC? Weekend parking will be easier, as weekday spots are filled by commuters usually by 8am or so. But it's easy from Chantilly to get to the Vienna station via I-66.
And just making sure you're aware, Manassas and Mt. Vernon are in two separate directions from this location, with Manassas being the closest. Both are still doable in one day if you want to make a loop of the area.
So if you're not bothered by the commute, this is a good base for your intended activities to the north, west and east. The area is safe and easier to navigate for an out-of-towner than some of the neighborhoods closer in.
Enjoy your trip!