FLIGHT - I would not do Sky express unless I were traveling with only a shoulder bag, and I assume you are using a rollaboard 20 or 21-inch bag. If you want to find out about Sky express' limitation, there's an easy way to find out. Don't ask us, go to the website. Take the 3.50 flight, and go across the street for a nice lunch.
ATMs - Of course use ATMs at Airport but use the Big Bank ATMS, like Alpha Bank. If an ATM machine asks if y ou want "dynamic conversion" Just Say NO. (that means it tells you in Looneys how much u are withdrawing, BUT it also means they charge a DOUBLE fee). Ask for withdrawal in Euros - you can do the math y ourself. When on an island, use the ATMs in a bank or right beside a bank. Others may be non-bank ATMs and charge big fees (just like the ATMs you often find in convenience stores or bars, in US or Canada.
LODGINGS & LOCATIONS -- In Santorini, I always recommend FIROSTEPHANI. It is at the North fringe of FIRA (the main town), but is walkable in 15 minutes to all the Fira attractions, yet has NO cruise-ship crowds or bus-groups, AND it has the lovely Caldera views of OIA (but again, not plagued by the ship-throngs that cram the Oia streets from 10am - 4 pm). In May for Naxos, I recommend staying at the Beach directly adjacent to Naxos Town ... again, because you can walk to the town attractions (cafes museums, shops, landmark sites), yet you are on a beach.
In ATHENS - I like the location just SOUTH of Acropolis, near the Acropolis Museum. It's walkable to almost all landmarks yet is quieter, on a wonderful long promenade along the south edge of Acropolis area. I am not going to recommend specific hotels in each of these because -- since you are very LATE in booking for May -- many of my recommends will be full. Instead, you advise that you go to Booking.com and put in your specific dates for each segment of your stay and search "Santorini FIrostephani" and Naxos St. George. For Athens, on booking. com there is a sorting process that will show you hotels that are close to a Landmark (in this case, Acropolis); I advise you to look only at hotels that are 1.2Km or closer -- this will assure that you don't get into faraway or "grungy" areas. Here's a "tiny url" for this: http://tinyurl.com/heq6edp
FINALLY (on hotels) -- when the list pops up, for any of the 3 destinations, just choose the top hotel and click on it -- that will bring up the Google Map for Santorini/Firostephani. Enlarge it, and you will see ALL the hotels that booking.com list in that area -- like little balloons. The RED balloons are fully booked ... the blue still have rooms. USE THIS MAP!!! it will keep you from jumping at a bargain, only to find that the hotel is actually way back from the beach, or the caldera, or the athens sights.
Good luck! And next time, start earlier.