If you must do Barcelona, start with a three nights there, then take a high speed train to Madrid (less wasted airport security time) - right now, Ouigo, a French company has started to compete with Renfe on several lines and they are selling CHEAP tickets (wife and I will go first class from Madrid to Barcelona for less than 70 euros next month). If the wife hasn't been, pick a museum or two (we like the Thyssen) and spend one night there before taking a train to Sevilla (if there is a way/time, you might squeeze a night in Cordoba to see the Mezquita). From Sevilla, after two nights (pro-tip: make a reservation to eat tapas one evening or lunch at La Brunilda - thank me later), rent a car and head for the hills (hill towns, that is). Ronda is the most famous and photogenic (if you like Roman ruins, on the way out of Sevilla, Italicus is worth a stop, some of the final scenes from Game of Thrones were filmed there). One night is enough in the hills and then it is on to Granada and the Alhambra. Give yourself a full day here, so two nights. Depending on the rental charges, either drop the car here and take a bus to Valencia or drive to Valencia and drop the car there. If your trip was early enough in March, Las Fallas would still be going on (look it up), but it will probably be past. Valencia is less visited, but has several UNESCO World Heritage sites and the spectacular, futuristic City of Arts and Sciences (which was in many episodes of Westward Season 4) and a great Mercado Central. I think it worth a night. From here, you can get a high speed train to either Madrid or Barcelona. Lots of jumping around, I know, but so many gems to see and enjoy.