In reply to nickh1964:
how will you be travelling from the airport? Rent a car?
Some options:
Barcelona - Cadí-Moixeró Natural Park is 2-3hrs drive from Barcelona airport. Never been there so I don't know what it's like or what the weather will be like at that time of year
Madrid -
Sierra de Guadarrama: is about 1hrs drive from Madrid airport. Some interesting walking. There's a big long ridge walk called the Cuerda Larga which is about 2-days' worth of walking or otherwise plenty of day walks. The highest top is Peñalara at 2,428 metres. The tops tended to be quite rounded. End of October could well be very pleasant. I'd be surprised if you had any snow that early. Lot's of ridge walks and the area of La Pedriza (famous for climbing) has some very nice walking.
Sierra de Gredos:
3 hrs drive from Madrid airport. A bit higher and wilder than the sierra de guadarrama. Sharp, rocky peaks in general. Almanzor is the highest at 2,592 metres.
Sierra Nevada:
accessible from Granada or Malaga airports. High mountains +3000mt. I don't know much about the area for walking to be honest.