What is the best way to get there? I will be traveling there the second week in September. How do you get from Girona to Begur without a car rental? Is a taxi expensive?
From Girona to Begur, Rome2rio.com suggests the Line 8 bus operated by Moventis or estimates 60-75 euros for a taxi (which might not include the cost of the driver returning home).
I found this web site with transportation information for Begur.
It appears that there is night bus service from Girona to Palafrugell (then taxi to Begur). During the daytime there seems to be some service from the Girona Airport to Palafrugell, but I couldn't turn up a timetable. I hope you're flying in, because it looks as if traveling from the airport is your best bet for getting close to Begur by public transportation.
I would caution you about depending on the last (or only) bus of the day for such a route. In almost two years of traveling around Europe (including Romania, Bulgaria and Serbia), I've only encountered one intercity bus that simply did not show up, and that was between two small cities in Catalunya. I was pretty shocked. I lost a 60-euro prepaid hotel room in Girona as a result. It was a Sunday, and there was little passenger traffic; the company may have decided it would lose money running that bus.
So I'd say be prepared to pay for a taxi. Or consider swapping out Begur for a more accessible destination. My trips have sometimes been about going to the most interesting place I can get to by bus/train rather than to the theoretically most interesting place.
Just ran across this post and wanted to jump in. We stayed in a house outside Begur a couple of years ago, flying in and out of Girona [which is also a pretty little city]. I do not believe one can stay in that part of Spain without a car. The towns are small and while we went to Begur every day, there is not enough to do to stay in the city for any period of time. The beach would be quite a walk away as it is a hill city and the return walk would be straight uphill for quite a ways. There are lots of great little towns up and down the coast, so I would highly recommend a car. Rental was no problem at the Girona airport.