When I was in 7th or 8th grade, a classmate pointed out to a teacher in one of my classes (geography? Spanish?) that there was a tiny country between France and Spain. The teacher refused to believe it until it was pointed out to her the existence of Andorra (468 square km), nestled in the Pyrenees between France and Spain. Since 1978 or thereabouts, I have wanted to visit Andorra, and if I'm going to Europe I'm going to try like hell to go there.
Unfortunately, Andorra doesn't seem to be easy to reach. Somehow, no passenger trains go there, only buses, so I'd have to get to the nearest train station (major cities nearby are Toulouse, France; Lleida, Spain; or Barcelona) and then take a bus. Given my itinerary, I could either get to Toulouse, take the bus to Andorra, and then the return bus to Barcelona, or go straight to Barcelona and make Andorra a day trip from there (which sounds easier as I wouldn't have to worry about my luggage).
The first bus from the Barcelona Airport to Andorra la Vella on either ALSA [go to Buy/Schedules > International for a schedule] or Andorra Direct Bus leaves at 6:15am and gets in at 9:15. Return buses are 15:00-18:15, 15:00-19:00, 17:00-21:00, or 19:15-22:30.
Once there, the TuristicaBus has four different routes [pdf map], depending on whether it's Tuesday morning, Thursday morning, Saturday morning, or Saturday afternoon (but based on when I'm in Barcelona, I can't go on Saturday). However, the tour buses depart Andorra la Vella at 9:00, so I'd have to catch a cab to La Massana (Tuesday) or Encamp (Thursday) to pick up the tour from the last embarkation point. The tours return at 13:35, giving me up to a few hours to look around Andorra la Vella before coming back to Barcelona. My choices are Tuesday Nov 15 or Thursday Nov 17.