What city is a 'must see' after our Western Med. Cruise

You will get lots of suggestions but I have always been fascinated by Spain's Moorish past so I would go for Sevilla or Córdoba...or for again something very different the area of Galicia.

More time in Barcelona, and then Madrid would make sense. There are a lot of day trips out a Madrid plus the city itself. If you tried Andalusia you might find that for practical reasons you have to fly home out of Madrid anyway. Your instincts to extend in Barcelona are good, because on a cruise (and my wife and I have done two Europe cruises) you often get only a whirlwind view especially with big cities. If that means less than a full week somewhere else, then I strongly urge Madrid. If you extended your stay in Barcelona by two or three days, that's too little time to do Andalusia justice but about right for Madrid. Plus the train there is a snap, three hours or less with no changes.

It you have a week, you could do as Lesley suggests - if you have time you should see the Alhambra in Granada, swing through Seville, a day in Cordoba, and finally Madrid. Fly home from Madrid. That is the significant history of Spain. You can do it all by train.

If you have plans to return some day for a more 'in depth' visit, then I would leave Andalusia for then.
Hopefully you can fly in to Barcelona one or two days before your cruise sets sail. Then if you have 7 nights post cruise ...
Day
1. Disembark in Barcelona (3 nights)
2.3. Barcelona sights
4. Train to Madrid (4 nights)
5. Madrid sights
6. Day to Toledo
7. Day to Segovia
8. Fly home from Madrid

Barcelona and the surrounding areas offer a rich vast menu of opportunities fully worth your exploration. Please consider renting an apartment for a week and utilizing the excellent public transportation system to access a variety of memorable experiences. The cruise will provide the experience of covering a wide amount of geography and spending a week in the Barcelona region will provide the ability to take a deep dive into learning a variety of experiences about the culture. To further define this opportunity I suggest creating a post asking folks what would they do with a week to explore Barcelona and the surrounding area.

About seven years ago we flew into Madrid, enjoyed three days there and then took the AVE to catch our cruise in Barcelona. Following the 12 day cruise, we spent five days in Barcelona. Great first trip to Europe.