San José: Tuesday, March 19th, is when
las Fallas de Valencia happen. Khaki's and a light jacket should be fine - if it's a sports coat (a little dressier) that might even be better. I wouldn't take any shorts. It shouldn't be that warm (although we had a call from Madrid Sunday and they said the weather was spring-like).
From those dates and the length of your stay It sounds like a spring break trip to me. Don't try to crowd too much into one week; just take the clothing you'll definitely need.