West Yellowstone, MT (WYS) is usually my first stop when I'm headed to the backcountry.
The airport has a Pilots Campground that is wonderfully maintained by the airport staff.
The campground has an outhouse, grills, a hot outdoor shower and mountain bikes available for riding into town (1.5 mi.) or just enjoying the surrounding countryside.
The FBO is run by R.J. and Sandy Moulton. They celebrated their 20th year at WYS in 2002. If you stop by, tell 'em John in Phoenix says hi!
I've visited WYS at least once a year since 1990 (except for '93 when Ol' Yeller died). It's a great place to stop if you want to take in the park, while avoiding the aluminum slums that the Park Service calls campgrounds. Rarely are there more than 1 or 2 planes using this beautiful spot.