1 week Honeymoon south of Spain

Beach or no beach?

Beach - Maybe spend the entire week in Barcelona with side trips to Girona, Montserrat and Sitges.

No beach - Spend 4 nights in Seville with a day trip to Cordoba and 3 nights in Granada or Madrid.

No beach this time....

Actually, Barcelona has beaches but you don't need to step foot on them to enjoy the city. It's a lot different than Madrid. Another option is to spend 3-4 nights in Barcelona and the rest in Madrid. You can take the fast train between the cities in about 3 hours. If you want to drive a bit, maybe spend 2-3 nights in Seville and then drive to Madrid via the White Hill Towns. Maybe spend the night in one of the towns (Arcos?) and then spend the rest of your nights in Madrid. You have a lot of options!

Kathleen,

Congratulations on your upcoming wedding!

Since you only have one week, I'd suggest choosing 1-2 locations.
The reason for this is so you won't waste time relocating from one place to the next.

There are various options for you.
I'd suggest you watch some of Rick Steves' videos here, and see what catches your eye.

I'd choose Sevilla & Córdoba., but that's just what I'd do.

Happy travels!

Edit to add,
Keep in mind that it will be hot in the South of Spain ;-)

I like Sevilla and Cordoba also, but since you plan on having a rental car, I'm going to throw a couple different places out there for your thoughts since you said you like culture. Santiago de Compostela to Leon. 2 nights in each city and then a night someplace in between, possibly Villafranca del Bierzo. If you another day, head down to Zamora for a night. While the list seems long most of the places don't take long to see. I've included things to see that I've researched for my upcoming trip there. Since you'll be traveling during the height of the tourist season you may want to have hotel reservations ahead of time. We're staying at Paradores in Leon, Santiago, Villafranca, and Zamora.

Leon
Cathedral, 5€ entrance (retired price), otherwise 6€
Historic center, plaza mayor, plaza san martin
casa botines - designed by Gaudi, no tours
plaza de grano, chocolateria valor leon
Museo Panteon, Basilica de San Isidoro de Leon, 5€ entrance, 1-hour tour
Astorga - look for shells on the street indicating the Camino de Santiago, walls like Avila.
Plaza de Espana and town hall- short stop
Cathedral - short stop. walls like Avila by the cathedral.
Ponferrada -
Castillo de los Templarios - De martes a domingo: de 10:00 a 14:00 a 16:00 a 18:00.
Torre de Reloj (close to the castle, plaza, and town hall
Villafranca del Bierzo
Castillo de Villafranca del Bierzo - a short walk from the parador, tours through the tourist office
Convent de los Padres Paules
Calle de Agua (a street with some old buildings)
Alto de Cebreiro on road LU-633 2.8 miles from Pedrafita.
The town itself, round Celtic hut, Church of Santa Maria
Alto de San Roque, on LU-633 2.4 miles past Alto de Cebrreiro
On the Camino, overlook, statue of San Roque will be on the left after going through Linares.
Vilar de Donas - on LU-P-4005 (1km off the N547), Church of San Salvador on the right.
Alto de Leboreiro - on N547, 10 miles from Vilar de Donas
Santa Maria de Leboreiro - on the camino, very small Romanesque church.
Melide - on N547 3.5 miles from Alto de Leboreiro. market town, known for bread and pastries
Cruceiro de Melide - oldest wayside cross in Galicia beside the chapel of San Roque. Is on the main road through town.
Monte de Gozo - Pilgrim monument (Monumento ao Peregrino)
Santiago de Compostela
cathedral, church of san francisco, plazas around the cathedral, old town.

Barcelona for the vibe, most definitely. Take days trips to Montserrat, etc.

Additional sight in Leon: Palacio de los Guzmanes. I was able to get an English tour, but I believe they are infrequent.

Additional sight in Astorga: Gaudi's Episcopal Palace.