This is a great question, and honestly, it doesn't have (for me) a clear winning answer.
One the one hand, driving around can be a nuisance, not only the roads of that area -particularly in August- are really busy, but also parking in the small villages and towns can be a nightmare (and expensive). On the other, a car/minivan would certainly give you the freedom to move about in that part of Catalonia. There are numerous things worth a visit, and without a car, it's rather cumbersome as buses -which are available- don't always conform to one's own schedule, if you know what I mean.
My advice would be: if you intend to mostly stay in one place and maybe make an escapade to ONE other town nearby, then stick to public transportation. Otherwise, if you intend to explore the area, a car is a must.
As per the road to Cadaqués (and a few others!), note you're driving in an area which is within a Natural Park (Cap de Creus), a protected area due to the exceptional biological, geological and scenic quality so the road has been adapted so as not to disturb it in excess. Yes it's a bit windy, but it's only for the last 15 miles or so and there's not much to it, it's a safe well paved and signaled road: https://www.youtube.com/watch?v=gMXR4GRle0w (courtesy of our Russian visitors, that seem to be in love with this thing about dashboard cameras, lol!)
Should you choose to rent a car/minivan...
Places nearby worth paying a visit -Google each for more info... most have their own "visitors' site" :)
... a bit beyond but worthwhile: Girona, Besalú and also three other nice medieval towns: Pals, Peratallada and Monells, they're relatively close to each other (video)
More info here: http://en.costabrava.org/
... and if you like music and classic arts, you can't miss dropping by the Festival Internacional del Castell de Perelada that runs for several weeks in July and August (note you need to purchase tickets in advance!)
For reference:
Map of roads in Catalonia
Routes in Catalonia
Enjoy!
PS: For added info, the county where Cadaqués is located is l'Alt Empordà... These are the counties of Catalonia, and for reference, Barcelona is located in the county of Barcelonès. Ah yes, we call them "comarques".