Thanks to so many of you for your very helpful recommendations. I decided (with some reservations, pun intended), not to stay at either of the Marriotts on the Costa del Sol, since it was in the interior regions of Cordoba, Granada and Seville that were of interest to me historically. I decided since it is both physically difficult for me and a real pain to move with suitcase and computer case between different hotels within a week that Cordoba seemed the most central and accessible to the airport in Madrid as well as the city of Seville. I'm staying In Cordoba for the whole time (except the last night at the Holiday Inn Madrid Airport), at the Hospes Palacio del Bailio, which looks wonderful.
So now I have more questions. It looks like I COULD rent a car with automatic from Madrid, but I don't speak Spanish (though can probably read it thanks to other languages) and have never before been in Spain. (It took many trips to France before I rented a car and sometimes I really did regret it, especially as I went round and round on the Boulévard Périphérique.) But it also looks like parking in Cordoba is tough, plus a drive to Granada sounds (from my guidebook) like hairpin turns on hills. So for anyone who has stayed in Cordoba or Seville, how is the best way to get to Granada? I'm hoping for excursions, and have emailed Cordoba's tourist office, but any advice? Cordoba itself could easily occupy two of my days, 1-2 in Granada, and 1 in Seville before returning to Madrid. It looks like there might be a more regular bus than train service to Granada in the event there are no scheduled tours. The hotel did advise me that I will be there partially during a bank holiday, which means many, many more people at the Alhambra.
Anyway, since I know several of you have 'done' Andalusia, can you give me some hints? Should I be utterly crazy and rent a car? Can I count on excursions from Cordoba? Or would any of you suggest a private guide if excursions are not possible?