What are the most authentic parts of Spain?

Hi, My husband and I are seriously considering moving to Spain to retire and to that end are becoming increasingly fluent in the language. We have both lived in different countries - UK, Italy, Canada, US - and don't see moving to a foreign country as a huge step. However, we don't know Spain very well and would like to move to a city/large town where we can consult or teach business English, while at the same time living in a villa rather than an apartment. We also don't want to be in a place that is over-run by tourists but has a somewhat quiet, authentic feel to it. We were wondering whether Sevilla would be a good place to head to but would value the opinions of some of the people on this site who have lived in Spain and know the country well. We don't think that we are Madrid or Barcelona people, so are interested in the places that still have a fairly thriving cultural downtown but aren't too crazy. Any suggestions would be most welcome! Thank you, Janie