Early spring and late autumn are when Barcelona feels like an actual city instead of a theme park. The summer crowds are gone, the Mediterranean air is mild enough for long beach walks, and you can see Gaudí's architecture without standing in two-hour lines.
A solid week from the US usually runs around $2400 for flights, stays, food, and entry fees. If you do not want to drain your savings account all at once, spreading that cost over time is easy to do if you stick to a simple plan.
Keep in mind that 0% intro APR is not free money; it is simply a strict deadline. If you do not clear the full $2400 balance by the end of the 15 months, the standard variable APR kicks in on whatever balance is left over.