A short hike to Delicate Arch (about 30-45 minutes) for sunset (bring a strong flashlight for the walk back downhill) is something you'll never forget.
Arches has a beautiful campground (see below), but it has no hookups. Landscape Arch is walking distance from that campground, and is worth the effort. You can see quite a few of the other arches with short walks from the parking lots along the road; if you start earlier in the day, you'll beat the crowds and bus tours that drive up from the town.