Another vote foe staying within the Park. If you need hookups, the concession operated Rio Grand Village RV campground is the only choice. If not, you can pick between NPS managed Rio Grand Village on the east side or Cottonwood (no generators) on the west. I'd guess you're too big for the Basin campground but be sure to drive up there, maybe take some of the hikes, have a meal and watch the sun set through the Window. We usually stay around two weeks and spend a few days in each of the three campgrounds managed by the Park Service.
Do visit Terlingua. The Starlight Theater has a decent menu and La Kiva is a great place for an adult beverage.