After a hiking trip in Portugal, DH and I are flying to Bilbao on July 9th, landing around 5:00 PM. We fly out of Bilbao early afternoon of July 14th. Only definite item on agenda is Guggenheim. Otherwise thinking we could divide our 5 nights between Bilbao and ? Looking to relax but not lay on a beach all day (some of the day is fine). Love food, wine, art, hiking. So many intriguing places, so hard to pin down. There's San Sebastian, St Jean de Luz, and even considering Rioja wine country like Logrono. Basically, want delicious food and wine in fun environment, with beautiful walks. Will use public transportation. Rick's Spain book is helpful...too helpful...as everyplace seems inviting. Thanks for suggestions.
Both San Sebastián and St-Jean de Luz are wonderful places to stay and explore. In France, drive up into the foothills of the Pyreenes and visit the small Basque towns such as Ascain, Ainhoa, Saré and Espellette.
I assume it would be cooler on the Basque coast than inland, in the Rioja. The heat would be my only concern.
I think you could have a wonderful 4 days between Bilbao, San Sebastian and the peninsula in between. The Oma Forest is a calm hike to a really unique art installation in a forest (stand on the metal arrows fixed into the ground and look at each grouping of trees from that perspective). The other interesting, though harder hike is to Gaztelugatxeko. San Sebastian is a nice mix of culture (Old Town, hiking (up to the Mota Castle and viewpoints on the hill), coastal walk, beaches and good food. That would be more than enough for the four days. But I haven't been to La Rioja (not a wine-o-phile), nor Logrono, so I can't compare
I´d stay in Bilbao and use it as a home base for Rioja Alavesa (the Basque Rioja, one of the three Rioja wine regions), as La Rioja is only wine country in the north (very few wineries in Logroño, which is in Rioja Alta and not that interestin) and it´s a political region (Spain is divided into 17 autonomous regions, similar to States in the US). Also, very good connections with Donostia-San Sebastian (many buses daily, one hour+ to get there), but if you can rent a car you have a beautiful route along the coast (San Juan de Gaztelugatxe, Mundaka, historical Gernika, Ea, Elantxobe, Lekeitio, Zumaia, Getaria (home to the first person that circumnavegated the world, in 1522, and of Balenciaga Dress Museum, and a delightful foodies place for seafood), Orio...
In Rioja Alavesa, Laguardia is a must, as well as Labastida and Elciego, beautiful centuries old wineries, and many with underground cellars built many centuries ago, making wonderful wines. Oma forest, as Jessica has recommended, is now closed and will be "moved" to another place, as it´s been badly affected by a fungus that kills pines, it can´t be visited anymore. St Jean de Luz, in the French Basque Country, is a very nice place, together with Bayonne. And Hondarribia, close to San Sebastian. Again, a car will be most helpful, although public transport is excellent.
One more thing: this is not the sunny part of Spain, it rains very frequently, it´s all mountains and beautiful forests and landscapes, and beach weather is not always a possibility (we have around 190 rainy days average per year), but July and August are the less rainy ones.
All the above place are good options. I think you might like the Rioja option. Especially if you are not into lying on the beach and are using public transportation. And while it may be a bit warmer than the coast, it will be less crowded and in general somewhat cheaper.
A possible itinerary:
Arrive mid day and spend the afternoon enjoying the old town, visit the churches and see the Michelangelo in the cathedral. You could go to Calle San Juan for pintxos.
Day three you could go to Haro to visit the wineries, or to San Millan to visit the UNESCO site and birthplace of Spanish. Both easily reached by bus. A less common excursion would be to Casalareina to visit the Monastery of Ntra. Sra. de la Piedad . By the river there is a nice picnic area, and if it is not too hot, there is an easy flat hiking trail along the river and through the vineyards, you might enjoy. For a farewell dinner, there are many good restaurants to choose from.
Day Four, return to Bilbao.