I lived in Greece for about a year. If you want culture, beach, and nightlife all in one, I would recommend an island. Mainland Greece just won't fit your needs. There are a few areas that have sortof what you want, like Nafplio, or Messinia, but overall, you will find more in Santorini, Mykonos, Rhodes, or my favourite, Crete. Starwood offers several luxurious accomodations in all three locations. Anywhere in Santorini or Mykonos will suffice. If going to Crete, I would recommend Agios Nikoloas or Elounda. I would stay away from Chania or Chersonissos (sometimes you'll see it spelled with an H instead of Ch). Crete offers several archeological sites, great beaches, and some spectacular nature. The Samaria Gorge is an absolute must-see, the food is great, and you can rent a car and drive the entire island without getting lost. There is really only 1 major road.
You can use your Skymiles to fly into Athens, then book a separate ticket on Aegean Airlines for the continuation onto the islands. Aegean is the best airline in Greece and intra-Greek prices are very affordable.
As for hotels using points, all three programs you listed have hotels, but only on the mainland. If you wanted to stay a few days in Athens before or after the trip, I would recommend just 2 nights. Everything you want to see and/or do can be done in 2 nights. The Marriott is quite nice and about 5 minutes from the city centre. It does have a free shuttle to Syntagma Square whch is quite convenient. The Intercontinental is basically next door to the Marriott. It looks like a nice hotel. The Hilton is kinda out of the way and is a very large hotel.
If I were you, I would go to Coupon Connection and see if someone would be willing to trade Starwood points for your Hilton/Marriott/Priority Club points so you can stay on the islands for free. Just my own recommendation.