On this thread, you are always going to get arguments for the Greek islands ... are you seriously asking us to choose for you -- or is this a ploy for us to give you a detailed itinerary?? Have you done any research yet on your own? IF you want an online resource, this is a good one https://www.greektravel.com/greekislands/
If u consult any AMerican travel agents, they will automatically say "Santorini - Mykonos" because those are the Cliche Twins for Americans who choose on the basis of travel posters, calendars, YOuTube etc (And also because travel agents get paid on basis of hotels booked, and these 2 have the costliest hotels]. And they are the MOST tourisized, MOST expensive of all the Greek islands, as well as the least authentic by now.
When you say "week-long" do you mean 7 nights?... fly out on the 8th day? If that's the case, you MUST be back in the Athens area for the 7th night... cannot chance missing your homebound flight. In that case its 6 nights -- and as 2 do-able islands for First-Timers, I would say SANTORINI (2 nights), NAXOS 4 nights.
SANTORINI - ARR athens, allow 2 hrs layover to domestic flight to Santorini. Get a hotel with balcony on the Famous Caldera View (that's really what this island is all about). Beaches are black grit, just really with purpose-built tourist settlements, not villages. View sunsets, visit village of OIA 8-10 am (to miss cruise crowds), and after 36 hours, take 3:15 BLUE STAR ferry -- large modern ship w open back decks for view.. a nice 2-hr mini-cruise to NAXOS.
NAXOS - Book seaview balcony room by St. George Beach, directly adjacent to Naxos town, easy 10-15 minute stroll to attractions of port town -- shops, cafes, museums, tavernas nightlife. Car rental or day excursion to explore dramatic inland landscapes, hillside viillages, ancient ruins, vineyards etc. 15 miles of golden sand beaches. Fly back nooonish of y our last day before Departure day, go up on Acropolis at 4 pm for sunset & have gala last dinner.