Those questions about weather are always a bit tricky to answer, because weather here is quite unpredictable. We´ve had the rainiest November since record have been kept (1947), that means 4 days without rain in Bilbao and 3 without rain in San Sebastian. SS is rainier than Bilbao and a bit colder, and February may be in the 40s, snow is also a (bleak) possibility. But this year (2019) we´ve had a sunny February, almost rain free, and temperatures in the 50s and 60s, with many sunny days. And freezing Decembers but wonderful Christmas on the 70s and sunny...the truth is that, while it´s true that this is Green Spain, you never know about the weather!! (sorry for being so imprecise...)

I would not consider SS as a resort town, it´s very far from it...it´s a working city with 180,000 inhabitants, lucky to live in a beautiful spot of the world. A city that happens to have three beaches, not a beach resort in any way. Worth the visit and the stay, that´s quite true.

Thanks for elaborating, Mike -- that helps cement the decision to split up my 4 nights.

I don't remember the specifics for these cities, but note that many places in Spain are closed all day on Monday and part of Sunday (not to mention their long midday hiatus), so if there are particular sites or museums you want to visit, make sure you check their opening hours before committing to a particular route.

For Monday-Tuesday in San Sebastán you won't deal with museum closures with the exception of the Museo de San Telmo on Monday, but Monday is a more limited day for dining than Tuesday-Sunday, but still there are plenty of places open.
The newly reopened, *wonderful outdoor (and indoor) sculpture museum, the Chillida Leku, is open on Mondays but closed on Tuesdays.
https://www.museochillidaleku.com/en/museo/visitanos/

For Bilbao on Wednesday-Thursday you'll be fine.

Ditto to Madrid on Friday/Saturday/Sunday (except for Sunday night dining, but still there are great places open in the Retiro district and elsewhere).
If you need specific dining recs, just ask, as we all have our favorites.

We finalized our plans with the help of all of your input -- thanks again, and here it is:

Madrid 3 nights (Catalonia las Cortes)
San Sebastian 3 nights (Airbnb: "Beautiful apartment in the heart of the city")
Bilbao 2 nights (7 Kale B&B)
Madrid 2 nights (Hotel Regina)

Our locations are fixed at this point, but all hotels reservations are refundable in case anyone has advice to the contrary about these choices. I am trying to determine if the construction in front of Hotel Regina is still ongoing; messaged the hotel many hours ago and waiting to hear back.

And Maribel, yes, I'd love dining recs from you and others!

Should be great!

Restaurants:
Bilbao: La Vina del Ensanche
San Sebastian / Donostia: Casa Urola and Restaurante La Muralla

Sounds great, GinnyJo.

My dining recs (moderately priced)--
Bilbao:
Ditto to La Viña del Ensanche (great Iberian ham)
Los Fueros (charming, Parisian looking bistro w/beautiful tiles, in the Casco Viejo for creative small plates fare)
Bascook (in an atmospheric former coal warehouse, great fusion cuisine & cool environment)
Los Globos for pintxos or small casseroles (cazuelas), next to La Viña del Ensanche on pedestrian Diputación in the Ensanche
Bar Gatz and Irrinzi near your 7 Kate accommodation in the Casco Viejo for innovative pintxos & Café Bilbao for classic ones on the Plaza Nueva in the Casco Viejo
Gure Toki on the Plaza Nueva (where we first met Fodorite mikelg--don't know how it's standing up these days)

San Sebastián:
Huge ditto to Casa Urola in the Old Quarter (the best of all)
La Muralla or sisters, La Fábrica and Urepel in the Old Quarter for good value
Antonio Bar (fantastic pintxos bar and 6-table hidden downstairs dining room downtown)
Casa 887 (new) in the Gros quarter
Narru (new location) with bar & restaurant in the Hotel Arbaso next to the Cathedral del Buen Pastor downtown
Jan Galerna in Gros (2 young, upcoming & award-winning chefs)

For a pintxos crawl...
La Cuchara de San Telmo, Ganbara, Tamboril, Borda Berri, La Cuchara de San Telmo, Bokado San Telmo in Old Quarter--they have kept up their high standards
Zazpi, Iturrioz, Narru's txoko downtown
Bar Bergara, Bodega Donostiarra and Hidalgo 56 in the Gros quarter

Madrid, within walking distance of your 1st hotel, Catalonia las Cortes in the Barrio de las Letras/Huertas area & moderately priced:
Vinoteca Moratín & Moratín 40 (same chef)
Triciclo & A Mano (same owners, members of the hugely popular Triciclo group--must reserve!)
Bodega de Mar (lovely seafood small plates)
La Malaje (sophisticated Andalusian fare)
Askuabarra (near Las Cortes, for great grilled beef from one of the country' best purveyors, Luismi)

Hope this helps!

Ditto to Maribel´s recommendations...and then there´s so many you will discover by yourself.

In Bilbao, bear in mind that 7 Kale B&B is in a pedestrian area, so if you´re driving or need a taxi, it´ll be complicated to get there. You´re going to love this trip!!

If you have just trolleys, it´s perfectly fine. This year they´ve installed cameras to avoid any entrance of cars in the pedestrian old quarter, but your taxi will leave you very close, no worries. Depending on the time of arrival, the taxi may enter the street (not legal, but kind of allowed). Great place to stay. Good restaurant area, and great pintxos at Santa María bar, one of my favorites.

I was going to suggest 3 nights in San Sebastian, perhaps the most beautiful city in Europe. All you need to do is print out Maribel and Mikelg's recommendations to have an incredible trip to the Basque country.

Beauty is apparently in the eye of the beholder. Pretty? In many ways, for sure! The most beautiful? Not in my book!