I haven't paid attention to private campgrounds in this area. There is a state park near Winthrop that may have hookups, but it tends to be busy and reserved in the summer. Next state park is out of the mountains (Raser).
The closest NF campground to Washington Pass is Lone Fir, which I've used several times. But the sites and loop road may be tight for a big RV. The Nat Park campgrounds are on the other side, Colonial Creek, and around Newhalem. Hookups, if anything, are limited.
Lone Fir and Colonial Creek are best for access to the trails. A couple of trails leave from CC itself.
