@GD... I believe you didn't mention "beach", did you? so yes, November is probably not the best time to go to "the beach", but for visiting the landscapes of the impressive Costa Brava it is probably the best time of the year since you'll find no flocks of beach-goers invading every nook and cranny of the area. My view, anyway.
Also worth noting Costa Brava is far more than "sea and beach", the area has magnificent landscapes, picturesque towns, historical sites... Besides, the weather by the coast is mild all year long, and in November temperatures should be in the high 50s.
Your best bet is to rent a car for a couple of days, so you can easily move around at your own pace. The area is worth visiting. If you find this town irresistible you can stay a little longer and if not just skip to the next one. That's my philosophy.
I am not fond of day tours presenting "Costa Brava" as this is a large area covering many towns, wetlands, national parks.... which can't possibly be visited not even in a full week. You're likely to be crammed on a bus most of the day and you'll hardly be able to experience much. Albeit, of course, you can also pick a single destination and go there by public transportation to spend the day, many suggestions come to mind: Vall de Núria, Girona+Besalú...
If you're still interested, please do some research here to focus on a few places and come back. I'll gladly help to create a route.
A nice video for a glimpse of Costa Brava here and also, for many more ideas, check here.
Enjoy!