If you are ok with a combo bus/train (Amtrak) tours, Amtrak has some fun trips to the national parks. We have enjoyed one tour and have used it also for planning our own independent travel.
For their options, see

http://www.vacationsbyrail.com/national_parks/index.html

Good advice - never gave it a thought. Thank you.

There are a couple bus tour companies that offer such options. One that I've used is AdventureBus:

http://www.adventurebus.com/

and one thing I liked about them is that you do get out and do some good hiking with these folks. Note that there is a roughing-it camping feel here for eating and sleeping, though I managed fine with it. I did the two-week Best of the National Parks tour with them that went to Zion, Bryce, Grand Canyon, Arches, Monument Valley, Yellowstone, and Grand Teton, plus days spent in Moab and Jackson. They offer other tour itinerary options as well.

There are other companies that offer similar tours. Note well that some apparently also offer a good bit in the way of hiking options, though reportedly others don't.

You'll likely get advice on this forum to plan your own trip, which strikes me as a good idea if you can do the driving required and don't mind making lodging arrangements ahead of time. If nothing else, you'll get maximum flexibility this way.