Suggestions for destinations to visit for 2nd timer?

You did not mention Barcelona, so if you haven’t been there, that would be my suggestion. There is a lot more to the city than the nightlife. Add Girona and Cadaqués on the Costa Brava and you have a nice trip.

It won’t help with beaches but any combination of the following cities Salamanca, Zamora, Segovia, León, Burgos, Santiago de Compostela, or Lugo would work. Travel time between them would be minimal. You may need a jacket in the evening.

By late September many of the smaller coastal towns between Cartagena and Malaga, and along the Costa de la Luz essentially shut down since tourist season is over. Many smaller hotels and restaurants close, so your lodging and dining choices will be reduced. I enjoyed Almería and its Alcázar but two full days is more than enough. To me, Murcia city and Cartagena can been seen in a few hours each. We once stayed at the Parador de Mojácar in late September and it was nice. It has a pool and is right across the street from the beach. Open restaurants were hard to find. We had a rental car.

Barcelona is must since you haven't been there before. I'd also recommend Valencia, which is easy to get to just down the coast a worth a few days. You might consider Malaga for a combination of history/museums and beach that has good train/plane options to get to. It might also be a good place to fly home from.

I think Barcelona and the Catalonia region in general will fit your bill. Culturally and historically distinct from the places you have already been to. Barcelona is still warm and sunny around September, avg is 26°C. So 12-14 days could be broken down like this:

4 days in Barcelona
4-5 days exploring the Costa Brava (base in Tossa de Mar)
4-5 days exploring the Costa Dorada (base in Tarragona)

PS: If you time correctly you can be in Barcelona during our annual city festival La Mercè, which will hopefully be this year on Sept 21-25 (God willing). In previous years the city wide festival had 100s of cultural events spread throughout Barcelona's squares, streets, museums, and parks. This is something that we put on for ourselves, not just for tourists and was a great opportunity to experience our Catalan culture like a local, at least for a few days. The best part it's free!

I only visited these because they were cruise stops, but I really enjoyed them - Cadiz and Alicante

If you can make it to Barcelona during La Mercè as Carlos suggested, go. We were there years ago and went to countless festival activities. My favorite were the castellers (human towers) in Plaça de Sant Jaume. The parades with fireworks should not be missed.

In my opinion Barcelona is Spain’s greatest hit. Buy tickets for the Sagrada Familia before leaving home. Good day trips from Barcelona are Montserrat and Figueres (Dali Theatre-Museum and another place you must buy tickets for before going).
From Barcelona you can take a direct overnight train to Donostia / San Sebastian and rent a sleeper car (7h). You can then get around the Spanish and French Basque Country side by direct bus from San Sebastian.
Good places to visit in the Basque region are: Bilbao (1h 15m by direct bus), St-Jean-de-Luz, FR (45-minutes), Bayonne, FR (1h 45m) and Biarritz, FR (1h 15m).

Barcelona and Catalonia won't let you down.

North to Barcelona
Girona, Figueres, Besalu

You can also consider an excursion into France. Perpignan used to be the capital of the Majorca kingdom.

Colliure is a small town which was home to many great artists.

While the consensus seems to be Barcelona, which I can't disagree with, a couple comments:

The other main region would be the Basque region with Bilbao and San Sebastian, lots of culture, beach, great food.

Another possibility, maybe with the Basque region, would be Galicia, way up above Portugal. Santiago de Compostela is the main draw, but the region features pretty wild coasts, and again, great food.

Aside from that, re-visiting at least one or two spots that were favorites is something I like to do. Seems the first time you hit the highlights, the second time you slow down and check out small things, and have some comfort in knowing a few good restaurants and shops to visit.

I have not been to the southern coastal parts of Spain but spent several weeks in various trips off the beaten track for mainstream tourism. I love Galicia. The food (esp. seafood) is amazing. I spent a few nights in Santiago de Compostela (the final stop of Camino de Santiago). Very nice and far less busy with big tour groups (pre-Covid). Make sure you have a Spanish hot chocolate at the chocolateria in old town SDC. One of the very best hot choc I have ever had.

Then, I spent some time in Orvieto, Woody Allen's fav town. Can't say that there is any imposing monuments to see there, but overall a charming place to chill and relax in.

The next stop was Burgos, also along Camino de Santiago. Again, beautiful place with less tourists. Awesome tapas scene.

Beach + history = Cadiz. We were there a few years ago and thought it was great. Pretty slow paced, great beach (for a New Englander, mind boggling was the notion there were places right on the beach where you could sit and buy and drink coffee. Does life really get better than that.) We also thought Antequera was an unexpected gem...and highly recommend Hotel Numero Uno and, dear God, also have dinner there. https://www.booking.com/hotel/es/meson-el-numero-uno.html

Just got back from Spain last month and spent 4 days of that trip in Cadiz, which was our first visit there. It's our new favorite city (I've been to Spain a bunch of times); we could have stayed a month. It is not a go-go-go kind of place, although there are sights to see, but it is great for walking, sitting on the beach, people-watching, eating (especially seafood). If you want to go back to Andalucia, you could plan a visit there.

You could also incorporate time in Malaga, and Jerez is an easy day trip from Cadiz..

Skyscanner is currently showing nonstop flights between Barcelona and Jerez and between BCN and Sevilla (both cities are on the train line to Cadiz) on Ryanair and Vueling, if you wanted to combine Barcelona with a return to Andalucia. Then you could fly back to the US from Malaga.

Hey Bark
I'm pretty sure you mean Oviedo in Spain and not Orvieto Italy.

@brad--thanks. made a typo. i used mostly my phone to reply to forum messages and it gets harder for my tired eyes to spot mistakes.

Barcelona!!! There's more to see and do in Barcelona than in any other city in Spain. Check out the TI website. Then there are a goodly number of day trips. And yes, Barcelona has lovely beaches. You could spend 2-3N in lovely Valencia. I haven't been (yet) but Zaragoza is high on my list.