Barcelona is all about walking past Gaudí buildings in the morning and losing track of time in tapas bars in the Gothic Quarter by night. To get the best mix of good weather and manageable crowds, you want to aim for shoulder season in the spring or fall. It is easy to spend a lot here if you book everything last minute, but a little patience keeps the cost reasonable.
A typical US traveler spends about $2400 on a trip like this. Spreading that out over time makes it much easier to digest, which is where payment tools come in. You can use the Discover it® Cash Back card, which gives you 0% intro APR for 15 months on purchases and balance transfers, meaning you get 15 months to pay off the trip without paying extra interest.
Remember that the 0% intro APR period is a hard deadline, not free money. If you still have a balance left on the card when those 15 months are up, standard interest kicks in on what is left over.