What are your favorite places in Spain?

After all the time spent in Spain in thirty years, I do not wish to expend my time on 'best' - as you still have so little time. You will have two tastes of Spain visiting Barcelona and Madrid. I suggest you look to the day trips which are available from these cities, which appeal to you and not me, again if you have time. There are fine guides to day trips in the Top Questions on the forums of Tripadvisor, as here -
http://www.tripadvisor.co.uk/ShowForum-g187514-i126-Madrid.html Good luck.

Spain is a big, diverse country. There is a big difference northern Spain which is more like Europe and southern Spain with the strong Moorish influence. My preference is for southern Spain because it is different. Barcelona and Madrid are similar being large more modern cities. My vote is for Seville, Granada, white hill towns, etc. but you don't have that much time. And Barcelona gives you a taste of NE Spain and not all of Spain.

Sevilla and Granada are places you should look into.

Since you are already planning to visit Madrid, it would be very easy to add Sevilla ( or Cordoba) and Granada ( our personal favorite because of the Alhambra). Travel between these places is easy and very comfortable.

Thanks everyone for your replies. I'm thinking Barcelona, Madrid, and Sevilla will be great starting off places for our first time in Spain.

Barcelona, Sevilla, and Granada.
Beach towns: Tossa De Mar, Cadiz and Stiges

Can Grenada be done as a day trip from Seville or does it require more time?

Same Granada for another trip. It could be done but the Alhambra is a full half day if not more plus Granada could be another day.