I would consider a day trip with Northern Alaska that is a flight one way and a drive the other way. Just to cross the Arctic Circle is a "been there, done that" checkoff item, but honestly just to drive there (which is prohibited anyway with most rental cars) is a pretty boring day. Best to make better use of your time and money by taking a day trip that includes much more. This originates in Fairbanks.
I have taken a day trip to Barrow, which was very interesting. I took it about the same time you will be going. I was able to take in a Barrow high school football game (famous for the artificial turf field they have - google it), walked around town a lot, took an ATV "tour" to Point Barrow, which is the northernmost point in the USA. There is an excellent museum in Barrow that is worth a visit.