Sitka is a good place to wander. The tenders let you off right in the middle of town. The Russian Dancers auditorium is right there and not expensive, but, if I recall, you must get the tickets right away and get off the tender 1st run. We only caught the tail end of the show which was enjoyable. The St Michaels Orthodox church was closed when we were there.

Skagway's walkable too. I'd still vote for the train (White Pass Rail) which would barely take you over your budget and you'd still be able to walk.