There is much riding (some easy, some technical) to be had up American Fork Canyon once the trails dry out. LINK TO PDF MAP
The main canyon road can get crowded and dusty with all the atv traffic so get there early on a Saturday. I have heard they may change up what trails are restricted to motorized so be sure to read the signage at the Tibble Fork trail head if you head up that way. There has been lots of anger lately from the mt bike community towards the motorized tearing up trails if its wet. Stay off the singltracks if its wet. The TW floats through most of it without rutting but its best to keep the trails buttery and smooth by staying off.
I have wanted to make a grand loop and ride up AF canyon to Midway, head over to Park City (via rt 222) and then up and over to Brighton ski area via Guardsman Pass. I have heard that you can ride up to Alta and/or Snow Bird but havent confirmed yet if you are passing through the lone peak wilderness area which would be a no-no.
There are a ton of double track roads around that lead everywhere. From Hobble Creek you can get to Diamond Fork, Sheep Creek, Strawberry, Wallsburg, and more. Then even further south is an area I would like to hit this summer and that is Skyline Drive above the Fairview area. There is just too much to see and do!!! Arapeen Trail Info
Other areas you may want to seek info on: Five Mile Pass, Cherry Creek, San Rafael Swell