You might have a better time by concentrating on a few areas and driving less, a mistake I often make. However, if in Tahoe, the Tahoe Rim Trail circles the lake with most of it open to bikes. Mr Toads Wild Ride is one I wish to ride there. Don't miss a descent or 2 at Downieville. 5000' descents in about 17 miles. Fun and beautiful. South Yuba was sweet but lots of Poison Ivy.
I've ridden amazing McKenzie River Trail east of Eugene, west of Bend. All I know who've ridden McKenzie and North Umpqua Trail (NUT) say the NUT is even better, 79 miles of trails broken into sections.
Haven't ridden much near Aspen, Governmnet Trail on my list. Maroon Bells is worth hiking to, in wilderness. Best at sunrise. Everything is sweet in Crested Butte, make it a focal point of the trip.
Durango has tons, check Trails2000.com for info. I love Phils World and Sand Canyon in Cortez.
Monarch Crest is an amazing 32 mile ride. As it gets above 12,000' do it late in the trip after some getting used to altitude. Hydrate, and not just beer! Above Salida. Most take a shuttle from Poncha Springs.
If it's cool head to Gooseberry Mesa and Little Creek Mesa, near Hurricane, UT. 2 world class trails that are more fun than almost anywhere.
Weather changes fast in the mountains, carry a rain jacket. Still monsoon season.