Logroño is reachable from anywhere in Spain by bus or train. The best options of relatively close airports are Bilbao (c. 1.30 h) and Zaragoza (c. 2 h).
Madrid is 4 h by train (RENFE) or bus (ALSA, PLM) from Logroño.
Barcelona is 4 h by train (RENFE) or 6 h by bus (ALSA) from Logroño.