This is a relatively moderate hike to truly amazing view. They call the summit "Top of the World" and it's well-named!
From Lime Creek Road near Vail pass, head up Bowmans Shortcut through forested hillsides. Run steep switchbacks to gain a wooded ridgeline. From large grassy clearings enjoy your first views of the Gore Range and the Ten Mile Range in the distance. Plunge back into dense forest for a long stretch of rolling ridgetop travel. Finally emerge into the aptly-named "Top of the World"
meadow for views of Sawatch Range, Gore Range and Vail's Back Bowls. Soak in the 360-degree views from this stunning alpine oasis, and either turn around here, or continue downhill to Two Elk Pass. This last section is very rutted with difficult footing in places and not particularly recommeded.
Once at Two Elk Pass, Bowman's Shortcut ends at the Two Elk Trail
(taking it to the west ends at Minturn, taking it east ends at I70 near Timber Creek). The unsigned Two Elk Connector goes north up Mongolia Bowl past Two Elk ski lodge and into the Vail ski area. Note: bikes are allowed on this trail.