Ten days is plenty of time
The ride from Anchorage to Fairbanks (346 miles or so on the Parks Highway) is an easy day ride. However, you may wish to stop at Denali National Park and spend some time, so make it two days. From Fairbanks to Prudhoe Bay, you can spend two to four days round-trip. From Fairbanks back to Anchorage, take the Richardson Highway and camp at Donnelly Dome or better yet, continue down to Paxson and ride in 24 miles on the Denali Highway to the Tangle Lakes and camp there. From Tangle Lakes, you can either ride back to Paxson and down to Anchorage in an easy day ride, or continue on the Denali Highway back to the Parks Highway and back to Anchorage, again an easy day ride. If you have one or two days left in the bank, from Anchorage ride down the Seward to at least Portage Glacier, or over to Hope. With enough time, ride down to Homer and back, but that's 6 hours down and 6 hours back, more if you take it easy and enjoy all the views. But probably just doing the loop will be enough.
Have fun!
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