It is about a mile from the Crossroads shopping center at the "end" of Hotel Plaza Boulevard to the Marketplace bus stop, so the Doubletree is less than a mile. I don't recall where the Doubletree is on that road.
I think it's definitely less than a mile from the Doubletree to the intersection with Buena Vista Blvd. A mile would probably get you to the Raintree. In any case be careful crossing that intersection -- it's not pedestrian-friendly.