Two hotels I absolutely cannot recommend enough:
Hotel Keti in Santorini
This is the view outside the room we stayed in at the Hotel Keti.
Hotel Omiros in Mykonos
I took this photo of the terrace at the Hotel Omiros while we were eating breakfast one morning.
Views that are worth a million bucks, prices at absolute rock-bottom. Plus at the Omiros, the owner, Yannis, is super friendly and chatted with us every day, giving us recommendations on restaurants and beaches, and his mom made us breakfast every morning. You really can’t do better than these two hotels.
Don’t miss a day trip to the island of Delos when you go to Mykonos, be sure to ask if Akrotiri is open on Santorini, definitely take a day to ride the donkeys down to the old port and take the sailboat tour around the caldera (the one where you hike up the volcano, swim in hot springs, eat an onboard buffet, and hear a saxophone serenade while you watch the sunset). Forget about wasting money on a travel agent, just do some research on Trip Advisor and make your own plan.
In Athens, obviously do the Parthenon and the Ancient Agora, but also be sure to spend some time at the National Archaelogical Museum. Just stunning marble sculptures that you could look at for hours.
And be sure to eat like there’s no tomorrow. Eat everywhere, we just took a Frommer’s guide and asked our hotel owners for advice and ate everywhere that was recommended and we were rarely steered wrong. Have Greek yogurt with honey, fruit and nuts for breakfast, and forget about the waffles (those are just there to appease French and American tourists – trust me, the yogurt is what you want). Eat with gluttony and abandon, the food in Greece is a rare treat.
[ETA] One more thing – we relied on the public buses in Mykonos and Santorini to get around. This was fine, and we never had any real problems, but if we did it again we’d definitely rent scooters and enjoy the increased freedom and reduced confusion/anxiety/crowding. In Athens, you’ll do fine relying on the subway, which is impressively efficient, accessible and clean.