YOu need 2 full days in Athens ...Best orientation on morning of day #1 is to sign up for the the well-regarded http://www.athenswalkingtours.gr/ -- their Main tour walks you thru the central athens area past many landmarks up the the Acropolis. Next walk down thru the Ancient AGORA, and out the south entrance to the Acropolis Museum. It's a great place for lunch, also on the terrace looking up at the Parthenon. BTW, Rick Steves website gives FREE AUDIO downloads of step-by-step guide to Acropolis/Parthenon and Ancien Agora, if y ou don't want to take a guide tour. For Day #2, He also has a step-by-step free AUDIO guide to the Top TEN sights in the Nat. Arch Museum (it's too far to walk - you take a taxi there & back), & his guidebook does it in print, and i think, his website too.
This website - http://www.planetware.com/tourist-attractions-/athens-gr-ath-ath.htm#GR107 (TOP 10 Tourist sights of ATHENS) will help you keep focussed & also has superb central Thens map to print out. Another website for Athens that you can "get lost in" is -- http://www.athensguide.com
Muskanm, you are spending a TON of money on this trip, so why not do some serious prep yourself instead of relying on random forum contributors to do your homework and make up your activity schedule for you? When you have a list of activities, you can ask our opinion for which are do-able and most worthwhile .... but we cannot sit at the keyboard and type out GReece 101. I suggest you run over to the library and get Rick Steve's Travel book -- it doesn't cover the islands but does a GOOD job of Athens highlights & 2-day activities for newcomers. Take it along. YOu can even buy a used copy cheap on Amazon.
The 2 islands you name are easy; small, very touricized (eveyone speaks English, u won't hear much Greek) BRotherlee has covered the main highlights of Santorini ... be aware that the beaches are NOT an attraction, so I hope you have a hotel w. a pool, if you want cooling swims.
In Mykonos, the beaches are sandy (and windy), and get ready for sticker shock at price of renting sunbeds & sunbrellas. What to do there? If you are interested in the island of Delos, do study up beforehand, or it will just look like a bunch of stones. Other activities? Beaches, taking pictures of the 5 windmills (not operative), walking around town admiring the architecture, having pricey drinks at cafes, staying up after midnight to experience some nightlife (only that's mainly July-August). And of course, shopping. Those beautiful white "cube" buildings along the lanes are now all shops for Famous Names -- Cartier, Hermes, DKNY, Hugo Boss, Calvin Klein, Dior, Chanel, Louis Vuitton, etc etc. For budgeteers like me, the best buys are the famous Greek Fisherman caps -- on this island, all the old Greek Guys wear them, and they're sold everywhere in small sidewalk displays ... and you cannot find them in most other island. Nor on most other islands can you find all those other International Famous Names .. mainly the few islands that have huge cruise ships docking, with eager shoppers!