Ritz Carlton tends to be the most pet friendly of the luxury chains. They generally permit well behaved pets to be in room alone.
Four Seasons generally requires that the pet owner be in the room with the pet at all times or hire a sitter when going out.
The Hay Adams is very good with pets.
The Acqualina Hotel in Sunny Isles Florida is extremely pet friendly, provides a very good amenity kit for pets, and makes arrangements to service the room while you're out..