Some good tips in this thread. Madrid, Sevilla and Barcelona are three wonderful cities.
Madrid: as many have suggested, Reina Sofia is worth the visit to check out te Guarnica and other works. This is a museum you can knock out in a relatively short time. El Prado has more stuff to see, I would budget slightly more time there (varies according to your level of interest in art). Plaza Mayor has plenty of spots to eat, though I would recommend going the tapa route…have something small at different places . The San Miguel is just to the West and probably a better food option than the places in the Plaza. As some have suggested, just walking around in Madrid is part of the experience. From your hotel to Plaza Mayor is a good walk: the Puerta de Sol area can get busy with all the tourists. Toledo is well worth a day trip from Madrid.
Sevilla: the cathedral, the alcazar and wandering around the streets are the highlights. Rooftop bars in the early evening can be great to wind down a day. This is a great spot for a flamenco show…I would shoot for places that have shorter shows (roughly 1 hour…think we went to a place called Casa de la Guitarra), but would have dinner elsewhere. The Alhambra is spectacular…well worth the effort (personally I would choose Alhambra over Toledo in terms of budgeting time).
Barcelona: a world class city with plenty of interesting places to eat. The private tour of Sagrada Familia is a must…skips the line and the guide will help you notice neat things. I’m not a big fan of the lower Ramblas, I find the part from Plaza Cataluña up towards Casa Mila much more vibrant and slightly less touristy. Having said that the Gothic quarter is kind of neat…the small Picasso museum has some interesting works. We loved Montserrat…takes up about half the day.