Vieste or Peschici as a base in late September?

We stayed in Vieste; I think this was during the second week of September.

We followed an unusual itinerary, beginning with a flight to Naples where we rented a car and moved on to Vietri for one night.
We then followed an itinerary that included stays in Maratea, Tursi, Matera, northern Puglia near Cerignola, and then on to Vieste.

Vieste accommodations are either IN the town or strung along the sandy beach stretching north from the town. We stayed in IL CASTELLINO RELAIS in a room with a large terrace. Hotels on that strip are across the street from the beach and our hotel gave us passes for chairs and umbrellas at a nearby lido where sea was calm and warm enough to swim. Hotel had free parking.

At night we either drove and parked in the lot below the town or, on one memorable night, had a spectacular dinner in a masseria restaurant with a farm in the hills above Vieste.

The town gleams with white marble streets and whitewashed buildings. Very few English speaking tourists when we were there. It IS quite tourist-oriented, with lots of shops selling foods aimed toward tourists and all the usual detritus you would imagine. BUT there is also vibrant local life in the piazza just outside the entrance to the historic core.....passegiata, families with kids running about, gelaterie---- and some excellent restaurants scattered among the more tourist-oriented fast-food-ish places.

There is another beach, just below the town where you could swim if you stayed in a rental or small hotel IN the town.

We only drove past Peschici; there are a lot of camp grounds and budget eateries along the road between the two...

I'm happy to offer any more tips if I am able...

From Vieste, we drove on to Termoli, one of our two destinations in Molise.....

We stayed at the Hotel Seggio, which is right in the heart of old town, and has a private beach. We had a room facing the beach, and it was wonderful. If I ever get back to that part of the world again I will absolutely stay there.

https://www.tripadvisor.com/Hotel_Review-g194948-d238467-Reviews-Hotel_Seggio-Vieste_Province_of_Foggia_Puglia.html

I prefer Vieste to Peschici. Peschici is perched on a hill top which makes it inconvenient if you want to spend some time on the ebach, and the historical centre is mostly shops selling touristy stuff. Vieste is perched on a headline, but just a five minute walk to the beach and has a 3-km long beach to the south which is excellent for walking, as well as promenades etc. There are also more shops like groceries, bakers, etc and more choice of restaurants. It has a larger all year round population.
However bear in mind that the season in the Gargano area finishes the weekend at the end of the first or second week in September, so you won't find many beach facilities open, although shops and most (the ones the locals go to so that's ok) restaurants will be open. Here's some more information:
https://slowtravelitalyspain.blogspot.com/2023/10/why-i-love-vieste.html

Here are some photos and details about what we ate:

https://www.hungryonion.org/t/gargano-peninsula-vieste/36074

I’ve always stayed in Vieste and visited Peschici from there (maybe 30+ min drive away.
Peschici is smaller than Vieste. Both are pretty.

Thanks to all of you who took the time to write quickly and thoroughly.

What Roberto said. I would just add that I loved visiting Peschici and wouldn't have wanted to miss it. I guess I'm not really a beach person, but I sure enjoyed staying "downtown" in Vieste.