Considering your interests (great food, hiking, beaches, nightlife unimportant) then Naxos should definitely be your other island. (And Naxos has many daily ferry connections with both Santorini and Athens.) Also, Athens needs at least one full day to explore so you should drop any thoughts about Delphi or Nafplio. Also, I would look into flights from Athens to Santorini on your night of arrival. If you could get to Santorini that night (and move your day in Athens to the end of your trip) you’d almost gain an entire day and could spend two nights on Naxos.
Can you see all the major sights in Athens in one day? No. But you can see the Acropolis, Acropolis Museum, and the top historical sites of the Plaka in one day. If you had an extra half-day then visit the Archaeological Museum in Exarcheia. That still leaves many great sights but you will have seen all of the iconic Athens attractions. Adding Naxos is always a good idea. You might even enjoy it more than Mykonos (but no nightlife like Mykonos).
– Any advice on where to go after for around 5 nights? Back to Naxos (we didn’t really move from the town last year unlike in Paros where we rented a car and saw the whole island)? What about Folegandros? Tinos? Milos? We would like somewhere with a nice town to walk around, upmarket, more couple less family, nice bars and things to see during the day bit also nice beaches etc?
Hydra is great but it does take a bit of time and effort to get to from the Cyclades. You’ll need to ferry to Athens, then might have to overnight there, then ferry to Hydra. Whereas Naxos, Paros, Milos, Folegandros, etc. would all be one direct ferry from Santorini or Mykonos. If you do go to Hydra then Leto Hotel is a great choice close to the port and shops and restaurants.
These groups are generally better connected among themselves than with other groups, so you are probably better advised to target them on this basis. As it’s your first time to Greece, you may want the full-on Greek island experience and you could easily fill your five weeks flitting from one island to the other in the Cyclades. You could start in Kea and work your way down to Milos via Kythnos, Serifos and Sifnos then segue to Paros and Naxos. Dip down to Santorini, up to Mykonos and back to Piraeus. The map will also show plenty of other Cyclades islands to pick and choose from such as Ios, Sikinos, Folegandros, Amorgos, Syros, Tinos and Andros – yes! too many choices, but you will find that sticking to one group it will be easier to get between them. Realistically for a period of five weeks you will not want to be doing more than 6-8 islands.