Vernal is ideally placed for day trips into the surrounding canyon country. Dinosaur National Monument, 20 miles to the east, is the obvious first stop — the Quarry Exhibit Hall lets you see over 1,500 dinosaur bones still embedded in the cliff face. The monument also has excellent hiking, whitewater rafting on the Green and Yampa rivers (with permits), and the scenic Harper's Corner drive.
Flaming Gorge National Recreation Area, 40 miles to the north, offers boating, fishing, and dramatic red-rock scenery along a 91-mile reservoir. The Flaming Gorge Dam is worth seeing for the engineering alone.
Further afield but reachable in a day: the Uinta Mountains to the west offer high-altitude hiking and fishing in summer; Kings Peak, the highest point in Utah, is accessed from this region.