X2 on bhoth's suggestions. In addition to Arches, the Island in the Sky portion of Canyonlands NP is nearby. Also We love the drive on route 128 out of Moab as far as Fisher Towers. The road is alongside the Colorado River and in a canyon. Feels somewhat like driving at the bottom of the Grand Canyon.
After Goblin Valley, drive route 24 through Capital Reef NP and pick up route 12 to Bryce Canyon. Route 12 is a spectacular drive. However, there was a post yesterday that a landslide took out a section of route 12 near Bryce, leaving only one lane open. Before you go that way, check current conditions.