I've had a long layover in Sitka before and although the town is fairly walkable, I would suggest renting a car from the Avis that is right at the airport--10 hours is a long time and probably worth it. This gives you a place to store whatever carry-on you might have as well as some protection from the inevitable rainy weather. I took a taxi from the airport to the Sitka National Historical Park with all the totem poles and after touring the park went to the Russian Bishop's House, then downtown Sitka, and finally ate the the Nugget Restaurant at the airport before flying out. With a car, you could probably drive around an tour some of the outskirts (and stay drier...lol). I believe Nome has a morning and evening flight if you're looking for another Alaska day trip idea.