I just had a friend return from a stay at Palms Place while he was at various horse tournaments at the Gold Coast and the Wynn. He loved Palms Place, and it didn't cost much more than the regular rooms at the Palms because it was slow. So since I found the regular Palms rooms okay but not more than that, I would recommend going for a cheap upgrade to the Palms Place rooms, which are suites. The $20 trick may work that time of year (non Fri/Sat).
Also, Red Rock rooms are pretty moderne, so you're in for a treat there, I think. Kind of upscale Star Trekkie.