I would suggest Zaragoza. This is the 5th largest Spanish city (654,390 inhabitants). It was founded in 24 b.c. by the Romans. It was the capital of the ancient kingdom of Aragón during the middle age. It has many museums, and lots of monuments like the wonderful Basilica del Pilar or the Alfajería Palace.

Zaragoza is the home city of the International Expo in 2008. For that reason the city has been completely renovated. The Expo Zaragoza 2008 will start in June the 14th and it'll last till September the 14th.

In October the have the great festivals of El Pilar.

The city is connected by high speed train to Madrid and Barcelona. It is connected by highway (speed 120 km/h) to:

Madrid --> 318 km
Barcelona --> 311 km
Valencia --> 312 km
Bilbao --> 305 km
San Sebastian --> 264 km
Pamplona --> 181 km
Burgos --> 264 km
Logroño (Rioja) --> 178 km
Cuenca --> 290 km
Pirinees mountains and French border --> 160 km
Tarragona (beaches) --> 238 km

So in less than three hours by car you can enjoy wonderful weekends in some of the most important Spanish cities.
You can also enjoy the festivals in Spain, like the San Fermines of Pamplona or Fallas of Valencia.
You can ski at the Pirinees in winter, swim in the Mediterranean in summer, and do some trecking in spring at the National Parks of Pirinees or Albarracín mountains.