Dear Ellen:
It 4 years now that I live in Spain, Last may I cycled from Madrid to Cádiz. It was a great ride. For your trip I recommend you to have in mind that Spain is a hilly country and there are some steep climbs and high hills even in Andalucia.
I recommend the spanish greenways, have a look at the site
http://www.viasverdes.com/languages/programme_english.htmYou'll find an overall map on:
http://www.viasverdes.com/mapa.htmAs destinations I recommend:
Granada, Seville, Córdoba, Cádiz
take care on the highways, specially on the coast and try to take the backroads, often much less traffic and beautiful scenery.
Any further question, let me know.
regards
sascha