Our experience in the Dordogne was too long ago to be of use now. Regarding the Basque area and down to Bilbao, I’ll set out below (lifted in part from my Chowhound posts back then) our most memorable from the Fall of 2018. (I’ve checked, and all are still open/ looking good.)
Sare/Sara, “Hôtel Arraya,” https://en.arraya.com/. The dining room is charming; the cooking is good, if not great. Dining with friends one night nearby at “Olhabidea,” owned by relatives of the Arraya, and just a few kilometers outside the village was very good (and they have nice rooms there, too). (Maybe Parigi will elaborate!)
Lunches nearby: Driving an hour inland via the Spanish route, we returned after a few years to have local trout under the 100+ years old plane trees next to the gurgling river at “Hotel Restaurant Arce,” http://hotel-arce.com/, in St Etienne de Baigorry. We look forward to this again some day.
We returned after a few years to “Hotel-Restaurant Ithurria” in Ainhoa, http://www.ithurria.com/, where we had dinner two nights, lunch outside at the bistro twice, and lovely breakfasts all three days. This family-run gem (two Ithurria brothers married two sisters) has been a hotel since 1962, when it was converted from a farmhouse. It’s had a Michelin star 50 years, since 1968. No “tweezer food,” tho! Standouts: Roasted Cepes; house cured (for 2+years) anchovies; local lamb and pork; pigeon and cheeses from Beñat. Oh, and 10,000 bottles in the cellar, including Sauternes at excellent prices. We will certainly return . . . .
Spanish Basque — and south to Bilbao:
Right across the border, in Hondarribia, we dined far from the touristy main street, up in the old town an outside in an alley at “Gastroteka Danontzat,” http://gastrotekadanontzat.com/ , and enjoyed it so much that we booked again for the next night it was open.
Lunch on the drive to Bilbao at “Kaia Kaipe,” Getria, in the corner window overlooking the working commercial fishing harbor. We had superb turbot for two, grilled in a metal cage over coals, along with a great Lopez de Heredia Tondonia Blanco, 2001. I just looked at the wine list again, and see it still has values — including for the impossible to find LdeH rosado (2011). http://www.kaia-kaipe.com/
In Bilbao, “Porrue,” http://www.porrue.com/?lang=en. This is * Michelin, and there were some tweezers used here and there, but I’ll mention it anyway, because it was perhaps our favorite restaurant of the trip. The excellent nine dinner course tasting menu was a bargain 68 euros per person. And on top of that, Pourre offered — and we took — an astonishingly inexpensive 28 euros-per-person wine matching for each course. Nine different wines for nine different courses. Generous pours in good Austrian stemware. They were very good to excellent wines, and the staff left the bottles on the table, in case we wanted more of any. Our first dinner there, and lively discussions with the staff and chef Unai Campo, left us excited and eager to experience it again, and so we returned the next evening. When we had dinner again the next night, and created our own tasting menu, the experience was, if anything, even better. (We enjoyed this more than the vaunted and too exclusive “Asador Extebarri,” inland, in Axpe on the drive toward Haro.)
Further afield, south of Haro (after a superb 2+ hour private tour and visit at Lopez de Heredia), in the quiet town of Ezcaray, we had a super lunch with scores of locals and no English to be heard at “Echaurren” (at its “tradition” restaurant), www.echaurren.com.