We did it, and recommend it. Just one night, and we stayed at the King Eider Inn, which is just across the street from the airport, and which I would highly recommend as compared to the other places we saw. You can walk the whole town in a few hours, and then we took an excursion in a Hummer to the Ocean. We saw plenty of whale bones etc. but no polar bears. When we were there, Barrow was "damp" meaning that you can bring alcohol in, but you can't but it there. So if you want a nightcap, you might want to get something in Fairbanks. Maybe it's changed since then. When we went, you could still carry on a bottle.