I've heard that the U.S. Park Service sometimes calls Bryce Canyon a cave without a ceiling, or a forest of stone. What I would call it, however, is the Grand Canyon without the crowds - every bit as beautiful, but much more remote, and the best vacation you'll ever have in your RV. Bryce Canyon is the perfect place to relax and get away from it all.
A beautiful way to begin your journey is to make your way to Monticello, Utah (a town that was founded by Mormons in the late 1800s), and start there. Head south on 191 until you come to Edge of the Cedars State Park. Edge of the Cedars is a wonderful place to go if you are interested in ancient Anasazi or Pueblo Indian ruins. There is no place to camp here, but there are several campgrounds nearby, and there are RV parks in Monticello, Bluff, and Blanding.
Turn west on highway 95, and you'll come to Natural Bridges National Monument. Here you'll find three natural stone bridges that span the width of sandstone canyon walls. These bridges are thousands of years old, and formed when water eroded the rock beneath them, creating the canyon itself. But the monument is more than a natural wonder - it's also the site of ancient Pueblo ruins, left by Native Americans who lived in this area hundreds of years ago. You can see ancient kivas, and the middle bridge, Kachina Bridge, also has petroglyphs and pictographs. Expect to spend at least two or three hours to explore - more if you like to hike.
Keep following 95 until you get to Hanksville (about two and a half hours from Monticello), and then turn west again on highway 24. You'll pass through Capital Reef National Park. Are you starting to feel like the whole state is made of state and national parks yet? It should be! - and you'll see why. This part of Utah is full of unusual geological phenomena. At Capital Reef you can find a 100-mile long monocline - a wrinkle in the Earth's crust, called the Waterpocket Fold.
Head south on highway 12, and you'll be in the Bryce Canyon area proper. It will take you almost two hours to get to Boulder. Near Boulder, make sure that you take time for the Anasazi State Park. This ruin, occupied from around A.D. 1050 to 1200, was once one of the largest Anasazi communities of ancient times.
Further down the road, you'll come to Escalante, and the Escalante State Park. One more natural wonder: a petrified forest. You can hike through the forest, go camping along the banks of the Wide Hollow Reservoir, rent a canoe, or go fishing. If you want to camp here, you can - there are several RV parks in Escalante, and a few more in Torrey.
In Cannonville, you'll come to Kodachrome Basin State Park (a little less than an hour's drive from Escalante). Why is it called Kodachrome? Because the sandstone chimneys here constantly change color, depending on the time of day and the weather. You'll want to take pictures.
Shortly after passing Tropic, you'll come to the turnoff for Bryce Canyon National Park itself. Turn south, toward Bryce, not north toward Antimony (though that way is beautiful too - it's just not Bryce). Getting to Bryce from Tropic will take you a good two hours or so, assuming that you don't stop along the way to admire the gorgeous scenery. Once you arrive at Bryce, be prepared - you are about to see one more completely unique geological sight. Not only is the canyon itself unique, but you can see plant and animal life that are unlike anything you will find in less remote areas. The changing elevations of the canyon walls support more than 400 species of plant, more than 160 species of bird, and you can also see mule deer, mountain lions, coyotes, marmots, etc. You can also see Utah prairie dogs, a threatened species that lives only in southwestern Utah. Don't feed any of the animals you see, but do take pictures. While you are here, take your time - go camping, bird watching, horseback riding. I predict you'll never want to leave, but most of us have to at some point.
After you leave Bryce, get back on highway 12, and head through the Red Canyon area for another unique sight - canyon walls that are literally red. You can go hiking here, but if you are here in the winter, you might prefer snowshoeing.
Then you'll have to make a choice - north toward Panguitch and Panguitch Lake, or south toward Hatch? South is the longer loop, but it will take you to Cedar Breaks National Monument and Cedar City, which will put you onto I-15, if you need it.
If you're coming from another state, and particularly if you are coming from the east, you may not realize it, but Utah is big. In these days of rising gas prices, you may find that you prefer to shorten your trip a bit. If so, you can easily spend a week at Bryce itself. You could do a shorter loop by starting in Richfield and following highway 24 until you hit highway 12. Then head south into Bryce, and afterward, take 143 past Panguitch Lake, or head south on 89 until you reach highway 14, where you can turn west for Cedar City. You'll miss a few things, but you'll still have a wonderful trip, and you won't have to fill up your gas tank quite so often.
One last thing - by all accounts, it's relatively easy to find Wi-Fi access in and around Bryce. But if you use it while you are there, you're a fool, and belong at home in an armchair in front of the television. Save the Internet surfing for when you get home. Nature has much, much more in the way of entertainment for you while you're in Utah.