From Capitol Reef follow Route 24 west. At the town of Torrey turn left (south) on Route 12 and follow it for 121 miles to Route 89. Along this magical stretch you'll wander through the Dixie National Forest before drifting into the northern fringe of the Grand Staircase-Escalante National Monument. Camping options are many. As are hiking opportunities, including access to some of Utah's famous slot canyons. Before reaching Route 89 you'll also pass Bryce National Park.
At 89 turn left and travel south for 44 miles to Route 9 at Mount Carmel Junction. Turn right (west) and follow it for 12 miles into Zion National Park.
Keep in mind that Route 12, due to its winding course, is not built for speed. Allow yourself plenty of time.