city for 2 weeks relaxation

You can fly into Madrid and take a direct train from Madrid-Puerta de Atocha to Ronda (4h) where you can sleep and rent a car to explore more of the Andalucía region in southern Spain. Great day trip options from Ronda are Arcos de la Frontera (1h 30m), Gibraltar (1h 45m), Zahara (45m), Grazalema (45m), Jerez de la Frontera (2h) and Seville (2h). A good day trip option by train is Cordoba (direct 2h).

You can drop off your car at the Málaga-Costa del Sol airport (1h 45m) and fly to Lisbon and change planes to get to Porto ($109).

Just because Segovia is such a charming small city, with its amazing Roman aqueduct, sights of its own, and great location, my first thought was of Segovia. It appears to have Europcar, Avis, and Hertz offices in town. It’s reachable by short train or bus from Madrid, and you’re not far from El Escorial and the Valley of the Fallen Monument. Relax on the plaza. Enjoy the signature roast suckling pig.

Leon came to mind followed by Burgos. Both are medium sized cities and not nearly as full of tourists as many other cities. There will be pilgrims walking the Camino on their way to Santiago de Compostela. Possible day trips from Leon to other cities might include Lugo, Salamanca, Zamora, Oviedo, Burgos. If you wanted to visit smaller towns, then Ponferrada, Astorga, Puebla de Sanabria (if there is train service to it), Valencia de Don Juan, or even Tordesillas. If you had a rental car there are plenty of very small towns you could visit from Burgos such as Santo Domingo de La Calzada, Ezcaray, Haro, Sajazarra, Chiuri, Lerma, and Casalarreina. It’s really just a matter of what you want to do with you time. If you’re a fan of the movie “The Good, The Bad and The Ugly,” there are a number of filming location from the movie near Santo Domingo de Silos, southeast of Burgos, but you’d need a car.

I get the impression you don't plan to have a car, so if you decide to take some day-trips, they will involve trains or buses. You've already had some good suggestions, but I think some are assuming you might be traveling around by car. Be sure to check travel times before assuming you'll have a whole slew of side-trip options from any one place.

I don't know how much of Catalunya you've seen on earlier trips, but Girona is lovely in itself (though certainly not undiscovered) and is also a good base for side-trips to places like Figueres (mailing for the Dali Museum), Cadaques, Besalu, etc. Those are all accessible by public transportation. I don't ride a bike in Europe, so I'm afraid I don't know how suitable Girona would be for that. The north end of the historic center is definitely not flat.

Galicia is another possibility. Santiago de Compostela is fairly centrally located within the region, opening up the possibility of day-trips to A Coruna, Betanzos, Pontevedra and some atmospheric, small coastal villages. Santiago has a large, attractive historic district. It gets a lot of visitors/pilgrims, but they are mostly concentrated quite close to the cathedral. The city is definitely not totally flat, that much I remember. There are ground connections from that part of Spain to Porto, though they aren't terribly frequent and may require a connection in the rather dull city of Vigo; as you may know, it's not so easy to get across that border if you aren't driving yourself or flying.

If you opt for somewhere in southern Spain, I'd try to start the trip there, as early in May as possible. It gets quite hot quite early in the year in Andalucia.

You've gotten some good suggestions for towns, my recommendations are more regions, which are centred around a main town, like Ronda, Cáceres, or Zaragoza etc.

White Hill Towns of Andalucia are a popular choice, albeit quite "on-the-beaten-path", it's certainly not undiscovered, if you get my drift ;-) You can fly in to Sevilla, rent a car there and then head up to Arcos or Ronda which make for fine bases, with Zahara and Setenil making for smaller more intimate experiences.

If coming from Portugal (or fly in to Madrid) you could consider Extremadura, just rent a car at Madrid-Barajas then drive southwest through the Extremadura region, a land of time warped Crusader Castles, Moorish Strongholds, Royal Monasteries, and impressive Roman ruins: stopping in places like Cáceres, Trujillo, Guadalupe Monastery, Mérida, Zafra. This is the region which the Holy Roman Emperor Charles the V retired to, it's also home to the best quality of Jamon Iberico in Spain.

Another region outside the international tourist radar is Aragon, fly in to Barcelona or Madrid and take the AVE direct to Zaragoza, from there you can rent a car and then tour this undiscovered corner of Spain. Center yourselves around Teruel, known for its Gothic and Islamic architecture, and then branch out to Albarracín (voted the prettiest village in Spain) and to ancient Calaceite. Also make a side trip to nearby Matarraña, nicknamed the "Tuscany of Spain".

Many thanks for the replies! Much to ponder...