What Ian and the rest said...
In Madrid:
- Do the museums Prado, Thyssen and Reina Sofia. In that order.
- Walk the Gan Vía and Plaza Mayor areas for tourist sightseeing
- Walk the Serrano and Ortega y Gasset streets for high end shopping
- If taking a woman go to Zara (cheap & chic clothing)
- Use the Metro (subway) to go anyware. Fast modern an reasonably safe
- Take care of your wallet. Pickpoketing is faily common (as in any other large city, think NYC) mugging is not
- If you have time visit Toledo, El Escorial and/or Avila (all three are 1 hour away by car)
- Eat "raciones" (portions) 5-10 € each. Try jamon serrano (cured ham) jamon iberico (the best quality cured ham, more expensive), chorizo (spicy sausage), morcilla (blood sausage), manchego cheese, calamares a la romana (fried calamari- onion ring style)
- Go to "El Corte Ingles", Spanish major department store. they sell everything. If possible visit the one in Castellana Avenue (the largest by far).
- Try the soccer match as suggested. In Madrid do the Real Madrid (best club in history) not the Atletico. the stadium is in the middle of the financial district. You can buy tickets directly there, no need to go to resellers unless they play Barcelona.
In Barcelona:
- Don't miss the Sagrada Familia cathedral. Amazing
- Go to Parc Güell for quiet relaxation
- Walk the Ramblas to the sea. Beware of pickpockets
- Walk the "eixample" (expansion) quarter. Nice geometric street design
- Be prepared to be spoken to in Catalan (similar to Spanish but not the same). however everybody speaks Spanish if you ask nicely
- Do soccer if possible. You want Barcelona FC (called Barça), not the Español
PM or email me if you have any specific questions.