Favorite Cities in Spain?

Hello. Going to Barcelona in April with my wife.

We are looking to travel to Madrid, Sevilla, Valencia, or Bilbao as well. We have 10 days total.

We are thinking of Barcelona->Madrid->Sevilla. We have never been to Spain. Are there any must see cities outside of these three? Or hidden gems we should try to go to instead? Would you recommend these 3 or others? Thank you