Vernal Utah is one of the hidden gems of the mountain bike world. You can come out and explore hundreds of miles of awesome singletrack without the crowds. You'll have several places to choose from, but this is a list of all the recommended rides.
McCoy Flats - No matter what time you arrive in Vernal you will be able to loop together all the different trails to suite your fitness level, skill level, and time you want to spend biking. I recommend starting with Retail Sale, then loop into Slippery When Wet. Depending on if you are tired or not you could also do Milk and Cookies.
McCoy Flats is just West of town on US40. You'll need to drive there, the shoulder of the highway is too narrow to safely ride to the trailhead. There are restrooms at the trailhead, but no water so bring plenty of water and food.
Red Fleet Trail System - Do the Red Fleet loop which combines Jazz with Jboy. This loop ends up being about 12 miles, and has around 1000 feet of climbing. it starts out with some flowy singletrack and has a few techy downhill sections.
After you are done with the trails head over to Red Fleet State Park where you can canoe, go fishing, relax on the beach, or go swimming. There are also some fossilized dinosaur tracks you can hike to.
Head up to Flaming Gorge State Park where you can go rafting, swimming, or hiking. The green river is crystal clear below the dam. They call it the aquarium because you can hike along the upper section and see tons of trout along the way. There's a good chance you'll see mule deer, elk, rocky mountain big horn sheep, and all kinds of birds. This would be a great hike for the kids.
Don't forget to bring your bike so you can hit Red Canyon Rim while you are there!
You've seen the larger trail systems, but there are still a few hidden gems several of which are my favorite trails. Drive North of Vernal on 3500 West to Dry Fork Canyon where you will find The Flume Trail. The Flume trail is mostly intermediate except for the lower section from the first to the second trailhead. On the lower section you will find advanced technical climbs, descents, log hops, and a small jump or two. This is one of my favorite trails, and it's a great way to beat the heat when its summer!
An alternative for more advanced riders would be Red Mountain Downhill West. Drive North about 5.8 miles from 500 North 2500 West in Vernal.This is a two track trail much like some of the chunky stuff you will find in Moab Utah. It is best ridden as a shuttle because it is a pretty technical strenuous climb to the top. You also have the option of taking the singletrack route down which is pretty technical and has a few big rock drops.
Don't forget to stop by Naples Country Grub and Vernal Brewery for burgers and beer while you are in town. I love the jalapeno burger from Country Grub. If you have any questions at all feel free to drop me a line.
For best results on this trip you could either bring a full suspension setup or a hardtail. If you are going to ride Red Mountain Downhill, or the lower section of The Flume I highly recommend a full suspension setup with tubeless tyres. One could still ride both on a hardtail but from experience, it's much more pleasant on a full suspension.
The setup I use to ride all of the trails in Vernal, Moab, and Fruita is a Specialized Camber 29er with 120mm of travel in the front and rear. I run a Specialized Purgatory up front, and a Specialized Ground Control in the rear both 2.30" wide. McCoy Flats is mostly hardpack with a small amount of slickrock. Red Fleet is hardpack with some loose sections, and some decent spans of slickrock. The Flume is a mix of loose and hardpack with roots, and rock obstacles. Red Mountain has tons of slickrock along with hardpack and a few loose sections.
I recommend having some type of sidewall protection at least on the rear tyre.