Imerovigli & Paros Recommendations Needed

I don't have any advice to give about Santorini; we've only been twice, mainly for logistical reasons, and anyway, we avoid crowds.

In Paros, we've stayed almost a month over the years. Naoussa is the part of Paros I hate, it's called the "little Mykonos." It's a very popular destination for wedding planners, travel agencies, and Instagrammers. In short, it's what we call a "tourist honeypot," (which I suppose is why you mentioned Naoussa).

However, I think it could work for what you're looking for, especially since it won't be too crazy in early June (though still quite crowded). The other option, if you're looking for a lively atmosphere, is to stay in Parikia, the port and capital. It's less chic and less expensive than Naoussa and a bit more "Greek." Furthermore, it's the hub for all the buses on Paros, in case you don't have a car.

If you're looking to swim, the beach at Naoussa is ridiculous (and windy) compared to the other beaches on Paros. Beach activities (swimming, diving, kitesurfing, windsurfing, etc.) are mainly found on the east coast, where the best beaches are.

Regarding wines, those from Santorini are world-renowned. You can find winery tours with tastings, or even better, you can go on your own if you have a car.

In Paros, right near Naoussa, there's a winery called "Moraitis" with excellent, internationally acclaimed wines. (Cheaper than those in Santorini)

https://moraitiswines.gr/en/mainpage/

And just 3 minutes south of Naoussa, there's also a local brewery, "56 Isles," which produces excellent beers and where you can enjoy a tasting:

https://www.56islesbeer.gr/

Regarding accommodation, you'll find many options. On the islands, don't focus solely on hotels, as they represent a minority of the available accommodations. Many places called simply "studios" or "apartments" offer the same services and comforts as traditional hotels and allow 3 or more guests to stay in a single unit. As usual booking.com, Google Maps, and Airbnb will help you find them.

In Paros in June, for two people, we never paid more than €150 per night in perfect accommodations not far from the beach and amenities. But we always rent cars. Without a car on an island, you lose more than 50% of your accommodation options and rates.

For fabulous view in Imerovigli, have a look at Villa Lukas or other accomodation in that very central location (look on google maps). I stayed there a couple of years ago and loved it.
In terms of Paros, unlike Jolui, I like Naoussa very much although I agree it has developed into a very upmarket village in recent years. However it is still, IMHO, an incredibly beautiful village and you are travelling at a quieter time. I would look at accomodation in the area of Agioi Anargyroi beach, which is not nearly as windy as Piperi beach I think Jolui is referring to. There are a wide range of types of accomodation for different budgets in the area. I often stay in that area, or very centrally and have never yet paid over €75! Its a quieter area and only a 10 minute eady walk to the village. Nearby great beaches are Ambelas (a few km in a taxi), or Kolymbithres and Monastiri accessible by boat from Naoussa harbour. For a beach party vibe, have a look at Punda and Santa Maria beaches on Paros as they may be what you are looking for. Hope you have a fabulous trip!

Haha!
I knew Missymoo would come and proselytize for Naoussa! So, in fact, that makes two votes for Naoussa, including mine, since I suspect that's what you're after.

Yep, I fell for it again JoLui!