Many of the tourist-oriented things are closing down for the year around Labor Day. That's actually true throughout Alaska. Maybe that is a sizable concern, maybe not too much of one.
Augustish was nice when I was in Fairbanks. A fair few years ago, in college, I visited a good friend who was then attending UAF (in Fairbanks) over Christmas and New Years. I would definitely recommend August over December; it's hard to actually see too much of Fairbanks in the winter since there's not much more than a few hours of twilight per day. It's also a good bit colder, of course.