Ok, thanks.

Is there anywhere along the southern Italian coasts in either Puglia, Calabria or Basilicatta?

Actually Malta is not a bad idea with ten days. It's quite built up around the capital Valetta (though there is lots to see and do there). The 'beach'/'resort' areas near there are rather crowded and built up but there are lots of other parts of the islands that are less so. I was there in summer and didn't notice any more British retirees than anywhere else. Probably they are more noticeable in off season. Here's my photos of Malta - https://andiamo.zenfolio.com/p217899981


If you go with the Greek islands I would substitute Paros (to pair with Naxos) instead of Mykonos if you want more 'chill' and less 'party'. Here's photos of Naxos and Paros - https://andiamo.zenfolio.com/p83290956

Apulia, Lucania and Calabria have tons of sandy beaches close to " gorgeous small towns to stroll in the evening" which will all be extremely crowded in August.
From August 8th until August 30th, most Italians will stay on their own beaches or on those around Italy (Ionion Islands, Croatia, etc.).

Actually, I'd do whatever Isabel says to do. Whenever I'm not sure where to go I go where she's gone.

There are some rather crowded sandy baches in the West of Malta (Mellieah and those close to the Gozo ferry), but forget the " gorgeous small towns to stroll in the evening" nearby.

What about the Balearics? I would recommend to check the flights from Prague (you can use https://www.skyscanner.it/).
Ibiza, Formentera and Mallorca are simply amazing and if you have, let's say 5/7 days, you can move around these stunning islands.
The weather is great and there tons of beautiful beaches amd bays to enjoy. As it's an archipelago and considering that the previous holidays are in european cities, i would also suggest to consider a boat charter. What i mean is that you can rent a boat (sailboat or catamaran) with skipper and sail around the Balearics, discovering everyday new spots reachable only by the sea and in the evening enjoy the islands.
I went there 3 years ago in September, we embarked in Ibiza and sailed to Formentera, that is closest island and then to Mallorca and Minorca. Amazing climate, perfect temperatures, fun and relax at the same time! What you think about it?

Thanks very much, I have now expanded my list

Here is the question I should have asked from the start:

If you had to choose one southern European (Mediterranean) place where you could base yourself next to a beautiful, sandy beach with warmer waters that is close to a gorgeous small town to stroll in the day and evening, but also be a destination where you can take interesting day trips to see historical sites, other beautiful villages and secluded beaches, where would you go (destination and town/village)?

I would go - and do go every winter - to Essaouira in Morocco. Why does it have to be in Europe?

Thanks for the recommendations. The only reason we were considering the Med is for the warmer waters compared to the Atlantic, which is a few degrees cooler, even in August.

However, you have my attention with Essaouira. Is it safe to travel on our own for day trips and is it near to nice beaches?

Is it safe to travel to Essaouira?

Why would it not be?

It's ON the beach, which is vast and beautiful. Yes, it can be windy and is therefore a major lure for kitesurfers. You can travel for miles north and south along the shore and all the beaches are pristine and uncrowded. Inland you can go to the mountains and the desert and beautiful oases; no shortage of daytrips or other towns and villages to visit. Even in mid-winter it is usually warm and sunny. In August it will be hot. You can rent a big, luxury apartment with terrace and sea view for a month or more for about 1,000 euros. The food is delicious and cheap. The enormous French Carrefour supermarket has everything you could find in any European city. The fresh markets are also bountiful.

Essaouira is on my short list of places to live in my dreams. On one trip a friend arranged for me to have a whole house with roof terrace in a quiet area of the medina . . . heaven.

If you look at many Government websites, Morocco does have a much higher safety threat rating than the other countries/islands mentioned due to threats of terrorism. Of course, terrorism can occur anywhere, but none of the other countries we have talked about have this rating. Of course, the chances of something happening is small, but it is a risk. However, I will look into it and thanks for the advice.