I liked Sevilla a lot, but its Spain's 4th largest city. That said, we didn't feel like we were in a big city. Our hotel was in the Jewish quarter close to the Alcazar which is a pretty amazing place to visit.
Close to Madrid, my ideas would be Segovia, Toledo and Cordoba. So if you want a taste of Andalusia, you could take a train ride from Madrid(I think about 2 1/2 hours) and spend your time in Cordoba. The Mezquita is amazing and the Jewish quarter where the Mezquita is located is quaint with the prettiest white homes with blue trim and courtyards/patios with lots of flowers. The only thing might be that it is starting to get warm that time of year so I would check typical weather for Cordoba.
I was just at Segovia and I thought the 1st century aqueduct was beyond incredible and the town is very quaint. The Plaza Mayor by the cathedral is a great place to people watch and I toured the Alcazar which was interesting but I enjoyed it very much for the views of the countryside from that area. But I'd be hard pressed to spend 3 days in Segovia. I'm not sure if its possible, but if you like the idea of staying in Segovia, you could look into train or bus service to Avila for a day trip. I didn't go to Avila, I would have liked to.
I also liked Toledo, tho I did think Segovia was "prettier and quainter". Toledo would be a good place if you enjoy the art of El Greco. I believe there were like 13 in the cathedral! There were other works by great artists, as well. Of course, the cathedral is beautiful and interesting by itself. We climbed to the top of the bell tower for great views of both Toledo and the cathedral. We also hired a taxi to drive us outside the city, across the river to get some views of Toledo up on the hill. Toledo also has a pretty amazing train station. I didn't do any research but it seemed to be a blend of mudejar and modernista architecture.
But, I'd be hard pressed to spend three days in Toledo, too. You said you don't enjoy large cities, but it would be pretty easy to stay in the old part of Madrid on the Puerta del sol and take day trips to Toledo and Segovia. Also within walking distance of Puerta del sol is the royal palace. I walked there one evening to see the exterior. It was quite pretty and all lit up.
All in all, if I were to have a vote (which of course I don't) I'd go to Cordoba and perhaps stop for a day in Toledo on the way back to Madrid.
In terms of food and wine, we had great meals and really good and inexpensive wines in Cordoba, Sevilla, Segovia and Toledo, so you won't have any problems there!