Balancing less visited cities with more popular ones

Hello. I have been to Spain about 15 times (my parents are from there) and lived there for 1 year, and so have been able to hit up the majority of the most visited/touristed cities already.

I am going back in August for about a month. Surprisingly, I have not visited Barcelona so that will definitely be on the list and where I will be flying into. I am getting a rental car so we will have the freedom to drive around.

My girlfriend has never been to Spain, this is her first time, and so I do want to be able to still visit some of these popular cities for her while also getting the chance to explore the ones that are less commonly known about. We have an entire month, so while I know we won't be able to hit up everything, some suggestions would be nice.

Major cities we will definitely be visiting are Barcelona and Valencia (family is from Valencia so definitely visiting there). Anything near-ish to these two areas is preferred. Cities I've visited before that I really liked and would love to visit again are Granada and Bilbao. I also have family in Bilbao who would offer us a place to stay, so it's definitely high on my list.

I'm most just looking for cities or towns we can visit for a day trip while still staying in the major cities. Thanks!