Bryce National Park, not unlike many other Utah national parks like Zion, Arches or Canyonlands Island in the Sky, is an in and out situation where you don’t drive through the park to get anywhere; at a certain point, the road just stops.
Like I mentioned, the shuttles run between the lookouts at the amphitheatre and this is very convenient if you plan to walk around the canyon rim because you can start at one end (either Bryce Point or the Visitor Centre), walk the rim, and catch the shuttle back without having to hike the same piece of land twice.
From here, you have the option of walking the entire rim trail but we decided to shorten it a little and get back on the shuttle for Inspiration Point, the next point and shuttle stop around the amphitheatre.
Inspiration Point is obviously just a slightly different view of the same hoodoos, but this time we took the Rim trail from Inspiration Point around to Sunrise Point.