Based on my travel experiences in Spain, I recommend going to Andalusia, Madrid, and perhaps Toledo. How many nights do you actually have on the ground? This was our itinerary for September 2017: Madrid (4 nights), Toledo (1 night), Córdoba (2 nights), Granada (2 nights), Malaga (2 nights), and Sevilla (4 nights) for a total of 15 nights. While it would have been nice to have an extra night in most places, I liked our number of nights and we were able to see and do a lot.
I chose Malaga for the coastal ambience. You have the beaches, if that is important to you. There is a wonderful cathedral but you certainly don’t have to visit it. We loved the Alcazaba. It’s a slow and wonderful walk uphill among ruins, lush greenery, flowers, fountains and small patios, with amazing views of the city, port, and Mediterranean. So that could be your nature walk. There is also a Ferris wheel for something different. Delicious fresh seafood!
And as others have mentioned, you can visit the white hill towns for country settings and getting out of the cities.
In Madrid, there is also Retiro Park, which is very pretty and relaxing. We sipped on sangrias for an hour at a cafe overlooking the lake. And you can take a rowboat/canoe out on the lake, too.
The Alhambra in Granada, the Mezquita in Córdoba, and the Alcazar in Sevilla are gorgeous and amazing, and I really don’t think you will be bored there.
If you like art, there are outstanding art museums in Madrid. Malaga, too, has many smaller art museums. I found the Picasso Museum to be very interesting.
Palacio de Viana in Córdoba and Casa di Pilatos in Sevilla are hidden gems!