You'll find plenty of cool mountain air, good fishing and awesome mountain scenery in the Timothy Lakes Basin. High altitude junkies will love this hike (or any hike in the Uintas for that matter) and peak baggers can gain even more elevation -- some of the highest peaks in Utah surround the lakes including Mount Emmons, the state's 3rd highest.
The trail immediately crosses Swift Creek, and directly on the other side you'll find a trail junction. Take the trail to the right (the trail straight ahead goes up Yellowstone Creek).
Brace yourself for a long, hot and waterless ascent. The trail switchbacks several times before topping out on the ridge, far above both Yellowstone and Swift creeks. At the ridge crest, however, the trail slowly contours to Swift Creek. After following the creek for half a mile you'll have to ford the creek, three miles from the trailhead.
Watch for the next creek crossing, one mile farther up the trail. Two miles more and you'll be at Deer Lake, six miles from the trailhead and a nice place to rest. Here, the bulk of the climb is over. (Unfortunately, the camping is terrible at Deer Lake unless you like camping on the dike next to the trail. Continue hiking to Miller Lake or the upper lakes for the best camping and scenery.)
About three-quarters of a mile after Deer Lake there's a trail junction, where you have the choice of going to Farmer's Lake or Timothy Lakes. You can't go wrong -- either trail is beautiful, and there is a trail connecting the two lakes. If you'd like to climb Mount Emmons, simply "route find" from East Timothy Lake. The best route is to head directly for the peak on Emmon's northwest shoulder. You should only attempt Mount Emmons if you're an experienced hiker or if you are in the company of one. But even experienced hikers should be reminded that the peaks in the Uintas are nothing but a big pile of boulders, tricky and fatiguing to climb on, and often loose.
Consider exploring the lakes just west of Farmer's Lake and below Bluebell Pass -- they're well worth seeing. If you have the time and want to see lots of trees, you can return to the Swift Creek trailhead by continuing over Bluebell Pass and going down the Yellowstone Creek trail.