There's an asphalt bike path from WP base to Fraser, in WP town itself, it's the sidewalk. It's about 5 miles long from the base to Fraser. It's downhill from the base to Fraser but at a steady grade. You can easily see the asphalt trail from US 40 when you're driving to Fraser.
In Fraser, there's good dirt trail that runs parallel to US 40 north to Tabernash. It's a couple hundred yards away from US 40 on the west side of the highway. You can pick it up near the rec center where the ice rink is. At one point, it does go through a cow pasture with a good many cows in there, but it's really no big deal.
Both of those routes are relatively flat for the area. The valley is about 8000'-9000' in elevation, so you will feel the altitude, especially on uphills.
There are trails and roads you can follow all over the place, but many of them have lots of hills so they're not as good for steady tempo work.
You can ask about more trails in the local bike shops or visitors center. They probably have maps there.