I would agree with Hawkman. In 2010, we flew up to Fairbanks to see our newest granddaughter in late Sept. Flew back in early Oct. The community outside of Denali was just about closed for the winter in late Sept. Still had some of the RV parks open along the Hwy. getting down to Denali, however. 
Have you checked 
http://www.rvparkreviews.com/regions/Alaska/Fairbanks.html?
There are often just pull outs along the Alaska highways in which people can overnight. We did an overnight at one (off the road a bit & up a hill with a parking area for viewing the vistas) not too far down from the Glennallen area towards Valdez on our way out from Chitina.
These might help:  
Free or Almost Free Campgrounds in AK  and  
Free and low cost camping in AlaskaThe 
Bear Lake FamCamp at Eielson AFB is a smaller cmpground, but in a wooded area with nice sites with water & electric, not sure of cost, just happened to drive by to empty at the dump site. But must be Authorized to use it. 
Haven't eaten at the  
The Alaska Salmon Bake, but hear it's a neat place next to the 
Pioneer Park in Fairbanks  Also $15 RV overnighting by the Park 
pioneerpark/visitor_information/rv_visitors.  
In trying to find a name for the food place, I found this 
Cafe offering a vast selection of unique Alaskan meals and wild game products. Might be good. 
What I have on 
Alaska. 
 :C  Clicky  :C  for a few photos.