Bryce is a pretty place to be sure, but there is really not that much to see or do there. The section that has the famous spires and ridges is actually a pretty small area - only a couple miles across - and there are only so many ways to look at it. There are some very nice 3-6 mile day hiking trails there, but if you are mostly interested in looking from the overlooks, you can pretty much see everything in a few hours. I don't know that I would drive the 7 hours from Phoenix just for Bryce.
I personally really love the Grand Canyon because it is so big, varied, and un-tamed. It is not really a single spot, but rather a whole region - one of the most rugged and unworldly in the lower 48. I have been there dozens of times, including many hikes to the bottom, and yet I still feel that I have only scratched the surface of its secrets. From Phoenix, the closest part of the canyon is the South Rim of the National Park north of Flagstaff and this is also the most developed portion with the most lodges, cafes, overlooks and shops. This is the place that most people visit and it does have some nice views and attractions, but be warned that it can be quite crowded from Memorial Day through Labor Day.
Canyon de Chelly National Monument is also a great place and different still than either Bryce or the Grand Canyon. De Chelly (pronounced 'De-Shay') is a winding sandstone canyon filled with prehistoric cliff dwellings. You can not really wander freely around the park, but rather there is a drive along the rim of its two main sections (de Chelly and del Muerto) to overlooks featuring views of the canyons and various ruins. You can do a short hike down to one ruin (White House), but to reach the rest you must go as part of a jeep or horse tour with a Navajo guide. This is the best way to experience the canyon (make reservations). Because it is so far off the beaten path, it is always pretty peaceful even during peak tourist season. There are a couple of small chain hotels nearby, but I prefer the historic Thunderbird Lodge near the entrance. Be warned it is a long drive to get there (much of it across unfenced range land on 2-lane roads). If you come up from the south, be sure to check out the historic Hubbell Trading Post in Ganado.
As far as other things between Phoenix and the Grand Canyon that are worth checking out...
As the poster above mentions, Sedona and the famous red rocks of nearby Oak Creek Canyon is a popular nature and new age spot (also lots of expensive resorts and galleries) and nearby Jerome is an old copper mining town turned tourist attraction. Both are neat spots.
In the same vicinity are Montezuma's Castle and Tuzigoot which are both prehistoric ruins (one is a cliff-dwelling and the other a pueblo ruin).
Further north on the way to the canyon, you will pass through the historic mountain lumber and railroad town of Flagstaff which is an interesting destination in itself. The historic downtown area has many interesting shops and cafes and the town is home to the excellent Museum of Northern Arizona and the Lowell Observatory (where Pluto was discovered in 1930).
Northeast of Flagstaff along 89A (which also leads to the eastern entrance to Grand Canyon at Cameron) are Sunset Crater and Wupatki National Monuments (so close that they are essentially one). Sunset Crater is an extinct volcanic field with lava flows and cinder cones while Wupatki is one of the largest and most scenic of the area's many prehistoric ruins. This is one of the lesser known local parks, but one of the best and most interesting.
East of Flagstaff along I-40 (which also follows the route of old Route 66) there is Meteor Crater (a big expensive and not that exciting in my opinion) and the Painted Desert and Petrified Forest National Park. The Painted Desert is a mostly driving tour through some colorful eroded badlands, but the Petrified Forest - with its rows of petrified logs - is pretty impressive. This is a smaller national park and both could be fully explored in a few hours.
In the small nearby town of Winslow, it is worth checking out the corner made famous by the Eagles song (Take it Easy) and - better yet - the wonderful La Posada Hotel. La Posada was built in 1930 as one of the last of the grand Santa Fe railroad hotels and has recently been restored into one of the best hotels in northern Arizona with a restuarant that is one of the best in the southwest and worth making a point of having at least one meal here.
Besides Bryce, there are also a lot of great places north of the canyon along the Arizona-Utah border such as the North Rim of the Grand Canyon (very different from the South Rim), Zion National Park (I would rate Zion over Bryce), Natural Bridges National Monument, Arches (Arches is way cool), Canyonlands, Hovenweep, Lake Powell and Monument Valley. However, these are all a long way from Phoenix and are best visited as part of a trip that focuses on that area (based out of Kanab, Moab or Springdale in Utah).
One thing to consider in your planning is when are you visiting. Northern Arizona and southern Utah are up on the Colorado Plateau at altitudes of 5000 feet or higher. Flagstaff and the South Rim are at 7000 feet and often get snow and sub-freezing temperatures well into April. The North Rim and Bryce are higher still (Bryce is up at 8000 feet elevation) and are down right bitter cold in winter (in fact, the lodge and other facilities at the North Rim of the canyon are closed mid-October to mid-May). On the other hand, if you are visiting in summer, the North Rim and Bryce are cooler and much less crowded than the South Rim.
All of the above places are great spots though and no matter which ones you chose to visit, you will be impressed.
Arizona resident, hiker, historian and roamer of the southwest. Grew up in Flagstaff and have been to all of the above mentioned place - many of them multiple times.
Some links related to the above places...
Grand Canyon National Park:
Bryce Canyon National Park:
Canyon de Chelly Links:
Hubbell Trading Post:
Zion National Park:
Sunset Crater and Wupatki:
Museum of Northern Arizona:
La Posada (Winslow):