March is better for Andalucia than Castille (south rather than north).
One possible exception that you may want to center your trip around is the Fire Festival in Valencia, March 15-19 in 2014. If you take in the festival, it will be an epic memory - and only happens in March.
If you do the fire festival, maybe start in Barcelona for 3 nights, Valencia for 3 nights, and Granada for 3 nights. Trains don't serve the Barcelona to Granada corridor well. A bus is the best cheap public transport option plus another popular local experience that is rarely shared by American tourists. The buses are very nice, like luxury charter buses here. Buses will get you anywhere. Each station I've been in has an information booth with an English speaker who will help you sort out your options and book your ticket. You can do the same at any local travel agent in town.
If you choose against the fire festival, I'd stick south. Fly into Granada for 3 nights and plan two nights in Seville (their festivals are in April, so you won't catch them). You can train between the two, but consider buses as a low cost alternative. I'd also plan at least a short stop in Cordoba to see the Mesquita and surrounding quarter (no less than four hours and use a taxi from the train or bus station to save time).
Some options if you stick south. Between Granada and Seville, you can bus to Ronda for a night, then bus to Gibraltar (probably La Linea, Spain) for a night, then up to Seville by bus (Jerez is another good stop). Cordoba could be a daytrip from Seville if you fly home out of Seville, or a stop on the way to Madrid if you fly home from there. The fast trains are great for Seville to Madrid (Cordoba between) or Barcelona to Madrid (Zaragosa between).
I could give you other options that include more stops in the north - but I really think you would kick yourself, because of the potential for very cold weather, if you choose north. Castille doesn't get the "soft" weather that Ireland gets. It can be bitterly cold along with wind, snow, sleet, freezing rain, etc. - much less than ideal touring weather, even if you're used to cold.