How long do you have for this trip?

Ad I think you need to check out the train web site to see what your options are. (Can;t help since we travel by car - find it much more convenient and gives the opportunity for serendipitous exploration.)

For suggestions on lodging you need to provide a specific budget in euros - and which hotels will be for 2 people - and for the other is you want one triple room or 2 separate rooms.

How long do you have for this visit and when in May is your trip? Depending on how long you have it may be nice to spend a couple of nights in Cordoba versus doing a daytrip from Sevilla especially if it's during the Patio Festival.

Do you plan on using public transport for the entire trip? Again, depending on how much time you have to explore it may be nice to get a car after Granada and have it to get to Nerja and explore this area. (I wouldn't suggest a car for the time you're in Sevilla, Cordoba or Granada though). But if you don't feel comfortable driving it's not 100% necessary.

"we can fly into Sevilla via American "
There are no direct flights from the US or with American airlines. I would make sure you do not have to change along this route somewhere.
If you only want to see cities then Train http://www.renfe.com/
also read this http://www.seat61.com/Spain-trains.htm#How_to_use_www.renfe.com
or bus http://www.alsa.es/
Some times even fly!

I think the OP meant they could connect into Sevilla via American airlines code share with Iberia. They'd arrive into Madrid as the original entry point.

We did some of your trip in reverse, going from the Spanish Pyrenees to Andalucia via Segovia, Salamanca, Caceres etc. So these pictures might give you some idea of organizing a trip in reverse, assuming that you wish to drive: http://www.flickr.com/photos/mksfca/sets/72157622975757180/show/

I don't understand the airline issue, there are many airlines that fly into Seville if you don't like American (which would be some codeshare). You can fly from lots of European cities without a stop in Madrid to Seville. There are airlines from London and from Paris, for example, that go direct to Seville.

Yes Christina, you can fly from a number of EU cities to Sevilla, but since the OP is flying from the States (from where, who knows), there are only one and two stop flights into Sevilla from Miami, Chicago, New York, Newark, Boston, Detroit, Atlanta, Charlotte, Los Angeles, San Francisco, Dallas/Fort Worth and Seattle.

Hello! I think Christina is right, and that it will be easier to land directly in Seville from another european capital town. Then what I can suggest, is to visit the area by bus (really cheap, and easy)if you don´t want to rent a car. You will be able to find hostels in each city to spend the night, but I suggest you book before you arrive. Then, from Sevilla or Granada to Salamanca, the best will be the bus (once again, train is quite expensive in Spain, and you always have to stop in Madrid...). You can have a look at this page: http://www.independentrip.com/39-espana/calculate-routes/75-salamanca_70-sevilla/ to know more about prices . For your stay in Madrid, you can have a look at this blog: http://ailmadrid.blogspot.com.es/2012/12/free-time-in-madrid-10-low-cost.html, and before you go back home, visit Segovia or/and Toleda (I prefer segovia!!) also by bus, Both cities are junt one day trips. ¡Buen viaje!