All hotels on the Hyatt page display the "from X points" message when you are on the first page of the search if you click "use points". Only when you see actually in the hotel specific search page does it tell you if points are actually available for use.
use.
I looked at the new Santorini hotel that came up yesterday to see if I wanted to try it instead of the secret suites, but it wasn't available. Appears to be in the center of the island with MUCH bigger (85 vs 35 sqm) rooms, but I think I'll stick with what I have anyway.