James:

Like George, although I have visited both Zion and Bryce several times, I too always stay in the campground. At Zion, I would recommend staying at the Lodge inside the Canyon. It is in a nice location and all the shuttles stop there. If you are staying at the lodge, you are permitted to drive your car into the canyon to the lodge. You'll still need to take the shuttle to get around the canyon floor though. Cost is a little steep. About $160 a night for two and $10 more for a third person.

If you don't stay at the Lodge in the park, I recommend you look for a place in Springdale, which sits right outside the park's West entrance and is only a mile and a half from the visitor center. There are free shuttles from Sprindale to the Park Visitor Center, from which you can catch the free shuttles that travel the canyon floor.

Approaching the Park from the East is not as convenient. Mt Carmel Jct is the nearest town, although there are some B & B's closer to the West entrance to the park. It is about 25 miles from Mt Carmel Jct to the Visitor Center. Plus, if your timing is bad, you could experience 20-30 minute delays at the one-way tunnel. Of course it is much close to Bryce.

In the past, I've always done Bryce as a day trip from Zion, although next time I'll camp so I can catch the morning and evening light.

Jim

Edit: There is also a really great bike path into Bryce from the Resort George mentioned if that is of interest to you.