Wiling to fly or train for a day trip from Barca. Any good ideas?
My recommendations would be to got to Montserrat. I don't know if you are religious but it is the place that St. Ignatius wrote his spiritual exercises. It is way up in the mountains (only reached by hiking or by a gondola) and has a beautiful church with a chior performing quite often. The views are amazing and there are absolutely great and breath-taking hiking trails. I would google image it and see if it looks like something you may be interested in. It is about an hour train ride west and is cheap/easy to get to. I have also heard great things about a small coastal town called Sitges which is also connected by train. Enjoy Barcelona!
I agree 100% with Montserrat, a great day trip from Barcelona and a hi lite of our trip to Spain. We stayed in Sitges and it is a nice beach community. It has a SANDY beach not PEBBLES. Lots of nice restaurants, shops and a short train ride into Barcelona.