we would like suggestions or day trips from Barcelona. We will not have a car, so there has to be a bus or train. We would also consider a one day bus tour outside of Barcelona. Any suggestions?

Haven't been to this city, but consider Montserrat, Sitges, or Figueres as possible day trips.

I recommend going to Girona for a day. I know there are trains that take you directly there, & I believe it takes an hour. We spent 2 nights in Girona in October & loved it!!!

We did several day trips when we were in Barcelona last fall:

Sitges -- pretty little beach town, short easy train ride

Tarragona -- interesting Roman ruins in a stunning setting, also easy to do by train

Dali -- My favorite bus trip was the Salvador Dali trip with Viator to the Dali museum in Figueres and Dali's home at Port Ligat. If you are a Dali fan, you won't want to miss this. http://www.viator.com/tours/Barcelon.../d562-3142DALI

Cava -- We also did a Cava and Wine tour that was alright, but I believe you can visit Freixenet on your own (via the train)

We did day trips to Girona and to Monserrat. Both reachable by train; I think Girona is the shorter trip. Girona is a walled sort of medieval city; it's pleasant, but I wouldn't describe it as overwhelming. Some nice views, as it's hilly, and a nice cathedral. Monserrat is very pretty. If you like hiking, it would be my recommendation.