Hi Randy
I'd like to echo Jane's recommendations, as well as visit several of the
places mentioned by Erik!
I'd also like to add the Jardi Botanic de Soller, on Mallorca. It's a short
picturesque train ride from Las Plamas.
http://www.jardibotanicdesoller.org/#_=_
Visiting the Parque Nacional de Ordesa y Monte Perdido may be a bit out of
your way, but it is spectacular, and a fairly easy day hike. There are other
national parks closer to Barcelona that are also nestled into the Picos de Europa.
If you like the artist Dali, then time permitting, visit Figueres, north of
Barcelona, Dali's former home and now museum/theater.
Dave Brastow