How far is the hotel from anchorage train station?

The Anchorage Hilton and Captain Cook are in what I would consider walking distance

I'm unsure what hotel you are speaking of specifically so it depends on where you are. The train station is right below the heart of downtown Anchorage. If you are staying in one of the downtown hotels, the station is about 5 minutes away by car or a 20 minute walk at most by any downtown location.