With that criteria my first recommendation would be Barcelona. Great city for adventure with a lot of options, depending on interests. Sagrada Familia, picasso museum, cathedrals, etc if that's what you enjoy. But also great neighborhoods, shops, and food, if you just want to wander. Montserrat is also a good day trip. Barcelona has beach options, but since it's a big city, there will be more people. Tons of options for a quieter beach all along the coast as you go south between there and Valencia. Tarragona is about an hour south, which would make a nice day trip from Barcelona. You could spend your whole time in eastern Spain along the mediterranean, and do a bunch of different things, if you wanted.
I love Madrid. Big city with some of the best art museums around, if you like that. Also the palace, cathedral, and other cultural things. Also great food from street food to Michelin star restaurants. You could day trip to Toledo.
We spent 2 days in Grenada because we wanted to see the Alhambra. We loved it. Not a whole lot more to do there, but there are markets and tapas places there.
Seville is fun with cathedral and moorish alcazar the two main attractions. But also a great city with narrow walkways to wander through. You could do a day or so there and then head south to Cadiz, which is on the southern coast. Could do beach time there.
Those would be places to start looking at, but depending on what you're looking for, you could look at the rioja region in the north and visit Bilbao. That would be close to Pamplona and San Sebastián, which is on the northern coast. There would be hiking and other outdoor options there.
I've done trips where I rented a car, and others where we've done only public transportation. Trains are great.
I'm happy to provide more specifics, or share what I can on places I didn't mention, that you might be interested in.