From Fort Bridger (WY), exit off I-80 and take Highway 414 south through the tiny communities of Mountain View and Lone Tree. At Lone Tree, the highway truns east. Follow the highway (SR 414) to between mile markers 132 and 133 and turn south onto FR 221. This is just before McKinnon. Stay on FR 221 all the way to Hickerson Park. At Hickerson Park, turn south on FR 001 and drive it seven miles to Spirit Lake. The road is usually in fair condition for passenger cars.
From the trailhead at Spirit Lake, simply head cross-country SE through the trees until you reach the crest of a very broad ridge-top. The forest here is pretty open and there is no bushwhacking.
Once on the gentle ridge follow it SW to "Dagget Peak" at 12,050 feet elevation. This is where you gain the first views to the south. From "Dagget Peak" continue along the broad ridge to the SE to a minor saddle. From the saddle, hike east to the summit of Eccentric. There are some boulders along the route, but as far as 12,000 foot peaks in Utah go, it doesn't get much easier than this.
The route is about 2500 feet of total elevation gain and about six miles round trip.
If you're after an all day hike, return to "Dagget Peak", but follow the ridge west from the peak. Follow the ridge west for about 2.5 miles (from "Dagget Peak") until a broad spur takes off to the north. Follow the spur north to McCoy Park. From here a trail heads east back to Spirit Lake, passing along scenic Tamarack Lake along the way.
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A good pair of boots is needed.