We spent a week tent camping at Coulter Bay last July. The campground without hook-ups never filled up, although there were only 3 spaces available one night. Coulter Bay is the only campground in GTNP that has showers, so my DW insisted that we camp there ($15/night). We saw a couple of TMs in the campground, along with many pop-ups and tents. The marina, showers, camper store, laundry, restaurants, and visitor center are all near the campground.
If you want hookups, you need to make reservations now for the summer. The Coulter Bay RV Park with hookups was full the entire week we were there ($49/night). Go to
www.gtlc.com for more info and to make reservations online.
We also checked out an outside-the-park camping option at the KOA in Teton Village between Jackson and GTNP. It was a fairly small and intimate campground, with mostly pop-ups and smaller camping trailers. There is a very nice wide asphalt walking and biking path that goes along the road for a few miles just across the road from the campground. I'd suggest calling ahead and getting more info if you're interested. The Teton Village KOA (tel. 307/733-5354) is 12 miles northwest of Jackson. Have a great trip.