If this your first time to Greece, I would invest one full day in Athens to visit the Acropolis and Parthenon, and then move out the islands.

In terms of the Greek beaches themselves many are somewhat rocky (not like Caribbean Sea sandy white). What makes Greece so special is the tranquility on the islands, against the warm blue Mediterrean waters.

I would recommend that focus your time in the Cyclades Islands, as you will get lower humidity levels than on the mainland, and a stronger sea breeze.

Here is a link to a map of the Cyclades:
http://www.mykonos-hotels.info/image...slands-map.gif

I prefer the Cyclades to the Dodecanese islands (Rhodes, Kos) as those islands hug the Turkish coast, and get meaningfully hotter in the months of July and August.

Islands like Mykonos, Paros, Santorini, Naxos are really magical, and should not be missed. You can easily visit many of the islands, as they are only a few hours apart by the daily ferries.

I have not seen many of the larger hotel chains on the islands, and I doubt they have many locations. Most luxury hotels seem to be independent, or are affiliated with a European label

If you're really set on using your hotel points, there are some great beaches in Southern Turkey with wonderful Hilton properties. I have stayed at Hilton hotels in both Adana and Mersin.