To get there, take I-70 about 3 miles west of Vail, and then take the exit for U.S. Highway 24 and head south a couple of miles to the town of Minturn.
If you stay on I-70 and go a little further west, there are some excellent places to fish right in the town of Avon, about 9 miles west of Vail. 3 or 4 miles further, you'll find some good fishing near the rest area just off I-70 (exit 163).
Another good place to fish is downstream of Edwards, the stretch of river where I-70 crosses over. Here you'll find about 2 miles of public water. Then about 3 miles down is the town of Wolcott. You'll find plenty of water open to the public from here all the way down to Eagle, a distance of about 10 miles.
Below Gypsum the river flows into the Bureau of Land Management public land, so there are lots of places to fish. To get there, use the service road that runs along the north side of the river. There are lots of places to park along the way.