Your trailer is small so towing on the Parkway should be no problem.The Parkway is much nicer than Skyline Drive and we towed the whole thing with our 25 ft TT.There are 2 campgrounds not too far off the parkway in the Virginia section which we really like.Towards the northern end is Sherando Lake.Has electric hookups,water hydrants in each loop,shower houses and dump station.It has 2 lakes one with a nice beach.The other campground which is a little more south is Goose Point.The one loop is right on the lake.Again electric hookups,bath houses and beach.A number of sites sit right on the edge of the water.