You're talking about a 30 mile ride to the Vedauwoo recreation area from Laramie. Mind you, it's a nice ride, but it doesn't leave a lot of time or energy to explore the area. There's any number of theoretical routes, pick your own and use a map.
The Vedauwoo exit is about 20 miles east of Laramie (and therefore about 25 miles west of Cheyenne). Vedauwoo proper is a picnic area with fabulous rock climbing and hiking opportunities. You can park in Vedauwoo and ride out of there, but it is best to cruise down the dirt road past the entrance to the picnic ground and turn off on one of the many side roads and park.
The roads (mostly double track) are largely crushed pink gravel. Compared to the Pilot Hill area, they're virtually highways. The scenery is spectacular and there is an immense number of double tracks to ride. There's usually a good race held here every spring. The start/finish area of the '94 race is shown in this picture. I haven't got any route in particular to suggest as I'm still figuring the area out myself (I got lost in the '94 race so how much do you want to trust me?). I don't think you'll be disappointed just exploring.
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Riding at Happy Jack
PT 12/97