Airports

The three closest airports to Palencia are:

Valladolid (Villanubla Airport, 45 km from Palencia): http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Valladolid/en/Home.html
(connections to Barcelona, Ryanair)

Santander (200 km): http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Santander/en/Home.html
(check destinations)

Madrid (Barajas, also Adolfo Suarez, 250 km): http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Madrid-Barajas/en/Home.html
(check destinations)

Madrid is the one with more flights to other countries and also with better conections (train, bus or car) to Palencia.