Cordoba is an hour by train from Sevilla: you may want to do it as a daytrip.
Sorry, I can't help you on Granada except to say it's somewhat further, not 'daytrip' distance.
IMHO, you don't need or want a car in the city of Sevilla; but you may want to rent one to do a two-day or so Andalucia 'loop' (Jerez de la frontera, Arcos de la frontera, Cadiz, Ronda, Granada, etc.)
Semana Santa is the first week of April, 2007 so March prices should be 'off-season,' but the good old days of 'everything's cheap' in Spain went out the window when the currency changed to the Euro back in 2001.
Eddie (native New Yorker)