Looking for a "luxury hotel near the water and within walking distance to a town" will considerably narrow the possibilities.
There are not really towns on the islands. There is a main town, often the one where the ferries arrive, but all the other places are villages of a few thousand inhabitants at most where you will always find bars, restaurants and a few shops and services.
Also, try not to focus on the term "hotel", luxury or not. On the islands there are many accommodation options of all categories that are not called "hotel".
Knowing that in this forum you will not escape being recommended to go to Naxos, I will list some other possibilities among those that I know:
The only option in Milos is Pollonia in the north of the island where there is a small beach, otherwise you will not find a beach within walking distance of the town in Milos. The southern half of Milos is a Natura 2000 protected area where there are no villages and very few homes.
Pollonia in Milos:
https://maps.app.goo.gl/4MwQ1viUNzZVg5uh6
In Parikia, the capital, there is a beach (not great compared to the others Paros beaches) or Aliki in the south of the island which is a nice little village / fishing port with an acceptable beach.
I do not recommend Naoussa in the north of the island which is very well known among Instagrammers, internet influencers and other sellers of honeymoon packages, it is a fishing village transformed into a collection of luxury boutiques. You will have already seen this in Santorini. Additionally there are only two tiny beaches facing north.
The best beaches of Paros being in the East, see the village of Piso Livadi.
From Paros you can go on a day trip to Antiparos
Parikia:
https://maps.app.goo.gl/3Nn5NKm6uFZRwMRW7
Aliki:
https://maps.app.goo.gl/ru64p3o3qcAwpYoYA
Piso Livadi:
https://maps.app.goo.gl/JvTWLVLTG67fezjH8
- Amorgos
Close to Santorini there is also the island of Amorgos, an exceptionally beautiful island which will make you regret having stayed so long in Santorini, where there are two possibilities: the villages of Katapola or Aegiali (I prefer Aegiali). There is a nice beach in Aegiali. The downside is that there is then a 5 hour ferry ride back to Athens
https://amorgos.gr/
- Sifnos
Sifnos can also be an option with Kamares, the port of arrival and especially in several others villages in the south of the island with beautiful beaches like Vathi or Platis Gialos. Sifnos is a 3-hour ferry ride from Santorini and brings you closer to Piraeus.
https://sifnos.gr/en/sifnos/