I stayed at the Fairbanks Princess in August of 2008, so my review may be a little out-of-date.
We spent two nights here, using Fairbanks as our base to travel to/from Barrow on a day trip. The hotel is quite close to the airport, probably only a 5-minute drive. It rained on both our nights here, which was a shame because one of the restaurants had an outdoor deck along the banks of the Chena River that we were unable to enjoy. I think there were three stories to this hotel in two different wings (one newer than the other). The lobby area was pleasant, with comfy couches, a nice fireplace, and game tables (there was another game/TV room on the second floor lobby). The rooms were standard chain hotel rooms. We had a king room that had a small table/chairs, chair/ottoman, sink area outside the actual bathroom, some minor toiletries provided, hair dryer, clock. Rates were low, so I would stay here again, particularly if flying into/out of Fairbanks (I think it was a bit far from the downtown area, though). There were two restaurants, as well as a bar/restaurant (Trackers, where we ate one night; good comfort food next to a roaring fire). The hotel gift shop is one of the nicest that I’ve seen, with a good selection of quality items, and also with a little deli/cafe bar and outdoor seating.