I've been to Naxos, Sifnos and Milos and either of those islands would be great. Since they are all Cyclades Islands most will be very similar in architecture, scenery and beaches with a little variation here or there.

Naxos would be #1 Choice to start with since it's the largest of the Cyclades and lots more to do, see and experience and in fact more varied topography and scenery.

Sifnos & Milos are very easy to combine.

August will be high season so most Cyclades Islands will be crowded, some less than others and also the most expensive time for accommodations.

Another combination would be Astypalea and Amorgos; Tinos and Andros or Syros; Aegina/Agistri (even though they are not Cyclades, they much closer to the mainland with Aegina apparently having everything one wants in a Greek Island and Agistri known for it's lovely beaches.

Lots of options so hopefully others will have recommendations.

Alll 5 Islands have sandy baches with cristal clear shallow water and places with low key tourism.
https://www.greeka.com/cyclades/

Naxos and Paros have direct daily ferries from Heraklion (Crete.
Twice weekly direct ferries from Rethymnon (Crete) to Santorini - Paros; connecting ferries to Naxos from both, Santorini and Paros.
Twice wekly direct ferries from Heraklion (Crete) to Milos.
Sifnos can be reached daily by ferry from Heraklion, with a ferry change at Santorini (ar 11.40, dp 13.35).
No ferry connection between Crete and Serifos.

Folegandros: sandy cove beaches, an authentic agricultural base, a regular public bus, good restaurants, one of Greece's best splurge hotels (such views!!), cliff scenery and what many consider a contender for 'most picturesque Chora' in that part of the nation.
I am done. The end.

Well Naxos and Paros are easily combined. Milos, Sifnos and Serifos are easily combined. You can certainly get from one of the first two to one of the second three but not quite as quickly. Don't know how much that matters to you. Naxos, Paros and Milos are large enough to have things (other than lie on the beach) to do for a few days. Actually Sifnos kept me entertained for 3 days. I felt like the Milos, Sifnos (also did Folegandros on that trip) islands were less crowded, certainly less Americans (as in virtually none). But I was there in July and people told me it got much busier in August. There is a fabulous round the island boat trip in Milos which has unique rock formations.



Here's my trip report from Milos, Sifnos and Folegandros - Greek Island Trip Report: Santorini, Folegandros, Milos and Sifnos in July


Here's the older one (2009) that included Naxos and Paros - From Santorini to the Peloponnese - Isabel's photos and trip report


Photos of all the Greek islands I've visited (including Crete) are here - https://andiamo.zenfolio.com/f320347206

On your list, we have been to Paros. Paros is a pretty little island. I would not say they had the best beaches. Also, it is small and not a lot to do there. We spent two nights there and it was too much.If you want complete relaxation, Paros is probably a great place.

Combine Naxos with ANTIPAROS -- small, accessed via little 10-minuteferry from PAROS. From its' tiny pier, totally walkable to sandy beaches. And y ou can go in for a day to explore the Port town of PAROS, then come back to Antiparos at end of day. The Antiparos "Agora" (Maze of winding lane with shops & tavernas) is lit up and magical at night. You can also book a day of water-fun on a boat, with swims & kayaking.

I agree with travelerjan that Antiparos would be a good combination with Naxos. It's very child-friendly, with most of the shops, cafes, and restaurants on a pedestrian-only main street. There are several gently shelving beaches within walking distance of the center of town. It would help to know what month you plan to visit the Greek Islands. Antiparos is quiet and laid back in May/June and September, but extremely busy in August. July gets busy when the Scandinavian schools break up for the summer.

The "tiny pier" that travelerjan mentioned is large enough for the excursion boats and larger fishing boats: Live Web Camera | Antiparos.TV .The dock for ferries between Antiparos and Pounta (Paros) is a little further along, and large enough for the three landing craft car ferries that run every 30 minutes throughout the day between Paros and Antiparos. Most businesses on Antiparos are run by year-round residents, as opposed to some other islands where they go back to Athens at the end of the season. If you want to see what Antiparos is like in July, have a look at this YouTube made by the islanders themselves:

I remember girlonthego's trip report from last summer. Had she spent more time on Paros she may have had a different opinion. Paros is larger than both Mykonos and Santorini, and attractions are spread out around the island. A good resource for things to do on Paros is: Paros Greece - Parosweb - Guide to Paros, Antiparos Islands

Rhodes and naxos would be nice choises

Elpida: if you are really a local, you should know that there is neither a direct ferry nor a direct flight from Naxos to Rhodos.