It's on Jamestown right across the East Passage from Fort Adams. You can walk up to the top of the cliff for a panoramic view.
Bit of a hike (over 2 miles) from Dutch Harbor but possibly worth it?
Walk back to the village and take the ferry for the post-race shenanigans. Maybe they will even have a ferry to Fort Adams. (I don't live there any longer or I would be of more help.)