You might want to take a look at my trip report for June 2011 starting in Bordeaux; click on my name to find it. Except for a walk over the border in Hendaye, our time in the Basque country was on the French side.

Kaixo! Take a look at Maribel's Guides to the País Vasco and the Pays Basque. They should help in planning your visit.

www.maribelsguides.com

Eskerrik asko, for the Maribel reminder ... all 88 pages of it!

I thought about starting in Bordeaux and renting a car, but don't want to return a French auto in Spain. After skimming Maribel and a couple of trip reports (thanks, Michael, great!), it appears that I should concentrate on Pais Vasco, and take a side trip to Biarritz and Bayonne.

Couple of interesting possibilities to add to my work-in-progress (Bilboa, Guernica, Hondarribia, San Sebastian) will be the Sanctuary of Loyola, and the Paleolithic cave art.

Late September / early October look good. Don't you just love the planning stage of a trip!

Be aware that the 61th edition of the San Sebastián film festival takes place September 20-28 2013. Hotel prices sky-rockets and you'll have to book early.

Fantastic city, the food capital of Spain, a rich culture that people take great pride in, beautiful landscapes, the finest city beaches on the continent and European capital of culture 2016.

Take a look at these very informative sites from Mikel from neighbouring Bilbao:
http://www.blogseitb.us/basquetourism/
http://mugalari.wordpress.com/

I think the Spanish side of the Basque Country is much more interesting than the French side, although the scenery there is beautiful. The towns of the French side are much more dolled up for tourism, and filled with tour buses. In France, I think nosing around the foothills of the French Pyrenees is more interesting than the French towns of the coast, but since you say you prefer the coast to the mountains, the scenery of the coast is really very lovely, you might find it rewarding.

For the Spanish coast, this is very useful:

http://www.spain.info/en/reportajes/las_villas_marineras_del_pv.html

If you have your choice of months you might look at June or September as brining hopes of more dry weather than rain, but fewer fellow tourists. If tourist crowds don't bother you, then I would definitely suggest going during July or early August.

Were it me going for 3 weeks, I couldn't resist adding time in the Picos, but I am more oriented to out of the way places. Rioja wine is one of my very favorites, and although I've no interest in visiting wineries, I would want to head into that area for meals and small town exploration and learning more history.

http://travel.nytimes.com/2012/10/21/travel/beyond-the-vines-in-rioja-spain.html?pagewanted=all&_r=0

I think this is a useful website

http://www.spainisculture.com/en/destinos/san_millan_de_la_cogolla.html

and this is exhaustive for the rioja

http://www.euroresidentes.com/euroresiuk/guides-spain/guide-to-rioja.htm

To answer your last question: Not really, but glad you are having a good time already.