Madrid is nice in early Spring:unfortunately residential heating doesn't end until 1 Apr,
so Madrid's air quality may leave something to be desired that week, especially if you suffer from respiratory problems.
San José is Mar 19: the Fallas de Valencia will have just ended when you arrive, but I have found that celebrations continue down the coast (Benidorm, Campello, Alicante) for at least a week (bullfights, etc.). They'll be 'marking time' until Palm Sunday (Apr 8) when there are 'Corridas' in Toledo and the Madrid area.
The weather should be pretty nice in Coastal Andalucia (and Sevilla, although that is their showery season). Having already been to Barcelona and San Sebastian, I would recommend about 4-days in Madrid (with day trips to Toledo and Segovia), and a trip to Andalucia: ours would be on a train called Triana to Cadiz - then buses to el Puerto de Santa Maria and Jerez de la Frontera as we work our way back to Sevilla where we spend 2-days before taking AVE back to Madrid to catch our flight home.
The Alicante thing I mentioned earlier is just if you want to 'kick back' and relax.