For Athens, I'd recommend Hotel Grande Bretagne. It's in Constitution Square and conveniently located to all of the major cultural attractions in Athens. The hotel itself is kind of weird looking on the outside (it looks like a big, square box with windows and pillars).

The fitness and spa facilities are top-notch. I think it's affiliated with Starwood because I was able to get points there (although it isn't a Westin). Of note, the Grande Bretagne has an excellent cigar bar called Alexander's. I have not dined there but The Cellar is supposed to be nice.