Here is The Traveling Professor's perfect Spain itinerary in 12 days:

Barcelona:  3 nights.  Barcelona is kind of spread out, so it would not be a bad idea to take the Hop-on Hop-Off bus to get an overview of the city. In fact, the city is so spread out there are 3 HoHo lines. Of course you want to see the famed Sagrada Familia but make sure to reserve in advance. La Boqueria market can't be missed as well as visit to Park Güell. There is nothing like strolling Las Ramblas and taking a tour through the Born area.  We like to eat tapas at Lolita's.  Our favorite hotels are the upscale Hotel 1898 on Las Ramblas. A little less pricey is the B-Hotel. 

Madrid:  Take the high-speed train from Barcelona and book it on my favorite train app, Trainline.com.  We love to stay in the center of the city at the Hotel Preciados.  Like most Spanish cities, it is great for strolling from the Plaza Mayor to the Plaza del Sol and just about everywhere else. Our friends at OgoTours run a great walking tour.  Great museums include the famed Prado, the Museo Nacional Centro de Arte Reina Sofía where the powerful Guernica resides and of course the popular Thyssen Museum.  Side trips to Toledo, Segovia and Avila are easy from Madrid.  Our favorite tapas can be found at the Mercado San Miguel and at the old style Taberna Los Angeles.  We recommend 4 nights in Madrid.

Seville:  Another train ride brings you from Madrid to Seville.  You can squeeze it all in 2 nights but act quickly.  We love all the walking tours by our friends APIE.   Visit the Alcazar, the Cathedral (Columbus, or at least part of him, is buried here), the Plaza Espana, and make sure to take in a Flamenco performance here. The Hotel Casa 1800 is the place to stay.  It's in close proximity to 2 of our favorite tapas spots:  La Tradicional and Bodega Santa Cruz.

Granada:  Again, take the train from Seville.  The last stop on your whirlwind Spain tour.  We recommend staying at Hospes Palacio de los Patos or Villa Oniria en Granada.  Of course the big attraction is the Alhambra, impressive as impressive can be. DO NOT miss it. Walk in Granada tours does an excellent city walk.