The section of the Colorado River that flows past Moab from the northeast - known as Fisher Towers - is one of the most popular venues for river-rafting in the whole of Utah. Whether you're looking for an easy day trip suitable for the whole family or something more adventurous involving a night under the stars, you'll float past majestic towers, between steep-sided canyons and - depending on how high the water is - through thrilling rapids.
If you go:
A number of outfitters run trips along this section of the river; Red River Adventures have a good reputation for helpful, safety-conscious guides.
Links:

Fisher Towers
Moab Utah 84532 USA
Mailing address:
Red River Adventures
1140 S. Main St.
Moab, UT 84532 USA
Phone Numbers:
Red River Adventures
+1 (435) 259-4046
+1 (435) 259-4046