With 4 and 1/2 days to spend in Andalucia during the second week of April 2014, it doesn't seem feasible to try to see all 3 main cities (Granada, Cordoba, and Seville). I'm thinking it makes more sense to see the 2 bigger cities of Cordoba and Granada. I will be taking a train from Madrid and prefer to take the AVE. Since it does not go directly to Granada, does it make sense to go directly to Cordoba, spend 2 days there, and then travel to Granada for 2 more days, returning to Cordoba to catch the return AVE train to Madrid? Or does it make more sense to limit the trip to Cordoba and Seville due to limited time? Also, I have not yet purchased tickets for La Alhambra and don't know if it is too late.
'I'm thinking it makes more sense to see the 2 bigger cities of Cordoba and Granada' - Seville is the biggest, Granada second, but agreed you cannot do justice to all three in this time.
It is, to my mind, either -
Granada - and Cordoba on the way to or from Madrid.
Seville (although Seville perhaps needs more time) - and Cordoba on the way to or from Madrid
you make Cordoba a long day and do not overnight and continue on to wherever
you go directly to Seville, stay all your time there and make Cordoba a long day trip, as many do. Seville to Cordoba by train is less than an hour each way.
'Also, I have not yet purchased tickets for La Alhambra and don't know if it is too late.' - then make a dummy run to find out or purchase now - http://www.ticketmaster.es/nav/landings/en/mucho_mas/entradas_alhambra/index.html
I believe there is a direct train from Seville to Granada. I would train from Madrid to Seville, stopping in Cordoba for a couple of hours to visit the Mezquita, then continue on to Seville. Then Seville - Granada - Madrid. It's about 5 hours by train from Granada to Madrid. There are only a few trains and buses (about the same time travel and about as comfortable) between Madrid and Granada. I'd decide on whether to start there or in Cordoba/Seville depending on the timetables.
Here's the Andalusia train route map http://www.renfe.com/docs/andalucia_MD.pdf