I have 6 days free in mid October and I'd like to see Barcelona. I'm on my own and think 6 days anywhere can get old. Should I also explore Costa Brava and if so, which towns would be worth seeing? Do I need a car? How many days in each have you found to be a good balance?
I loved Girona, about 90 minutes from Barcelona by train (there are also buses). My Let's Go: Spain called it "a world class city patiently waiting for the world to notice" and they were 100% right.
If you end up renting a car, the town of Roses in the province of Girona is very beautiful. It has some historical castles to visit and a nice church; the beach is pretty nice and if you drive a little bit outside of town there are many little charming coves.
The food is great too!!