I can think of two possibilities:
1. Any of the mountain towns will have river trails, either paved or a worst compacted gravel. Breckenridge comes to mind, also the trail in Glenwood Canyon. Most of these trails are currently under water, but by the 20th the snow melt should be finished.
2. For a flat road with awesome scenery, you can't do better than the Paradise Divide to Yule Pass road NW of Crested Butte. It's been closed to vehicles for ten years and runs flat at 11K for ~3 miles. Great tent camping at PD. The old road is not maintained so you'll have to deal with rock fall on the road.
Enjoy your trip.