Thank you so much for all your answers. There's a lot to choose from =)

Should we stick to one island (with Santorini) or can we do Naxos and Paros?

I plan to book everything in the next few weeks.

That's up to you, really. Santorini is unique, so that should be near the top of your list. Paros or Naxos would give you a different experience, far more relaxed, cheaper, and with some great beaches. I far prefer Naxos and Paros, and the latter gives you a chance to visit my favourite Antiparos.

In your OP you wrote: "We will have between 10 and 14 nights..." Try to stretch your trip to as long as you can — 10 nights will feel rushed for two islands + Athens, while 14 nights would be much better. It's your honeymoon, and you need some time to relax together.

If you decide on Paros, try to work in a round-island boat trip. The trips leave from both Antiparos and Pounta (the port) on Paros, and include a BBQ lunch and stops at beautiful beaches and sea caves on Antiparos and nearby uninhabited islets. There are several from which to choose, but one of the best is http://captainbenantiparos.com/#up