5 day road trip in Northeast Spain/Basque country

Stop in at our son's friend's bakery Kuki Cookie while you are in the heart of Billbao!

I don't think it's possible to fly directly to Bilbao from the US, so are you connecting
somewhere else in Europe, and if so, when do you land in Bilbao? That may be
relevant to consider how far you can drive after your arrival.

I'd consider staying a night or two in French Basque country (Sare, Espelette?)

Mikel can hopefully provide more expert insight, but some of the coastal towns may
be a bit quiet since the summer season will be over.

Laguardia is a lovely town for a night or two also.

This area was one of my most favorite trips, but this was 12 years ago. I split my week between the Spanish and French "sides" because for me experiencing both was part of gaining context. (On the other hand, I am fairly fluent in French and also taught history and like politics!)
I stayed the first night after arrival from the US near the border and used public transportation. I stayed in San Sebastian and a day trip to Bilbao mostly for the museum and hired a driver for the coast going south to___? (Sorry! But it's famous! And there was a good hike somewhere.)
I stayed in St. Jean de Luz and loved it. From there I arranged day trips (Sare, Esplette, Biarritz). If you have the time the Basque history museum in Bayonne was excellent.
You will have a wonderful time!

Answering your questions:

1) We'd like to stay outside Bilbao but close by on the first night after a long transatlantic flight.

Getxo, with its unique.-in-the-world Puente Bizkaia (a mile from my home), its beautiful promenade by the beach (although beach weather is not usually an option), and the picturesque old fishing port of Algorta, is a very good option. Close to Bilbao and very easy access to the city on public transport (underground -safest, cheapest, cleanest- or bus).

2) Suggestions of towns to stay in are very welcome, especially specific small hotels/AirBnB or rustic farm stays.

Check https://www.nekatur.net/en for this type of cozy, rural accommodation.

3) We aren't particularly into wine, but would consider going to the Rioja region for scenery or other worthwhile places to go. LaGuardia sounds like a must.

Laguardia (not LaGuardia) is worth a visit, as is Labastida or Sajazarra, for example. I would try to visit a winery that offers visits of the 15th ot 16th-century cellars where some of them still make wine. It´s ot being into wine, it´s history and how this area was shaped. Rioja wine region, divided into Rioja Alavesa (Basque), Rioja Alta and Rioja Oriental, should not be mistaken with La Rioja political region.

4) Is the Baztan valley worth a visit? Are the leaves changing colour in mid/late October?

This is mountains, green forests, water, trees...we have dozens of great places in the Basque Country for hiking and for trees, Baztan may be a bit too far (it´s in Navarre). Beautiful, but all the northern part of the Basque Country is a big forest. Gorbeia or Aizkorri natural parks will also be an excellent option, and much closer to Bilbao or Donostia/San Sebastian.

Yes, the leaves have already started to change colors. I was in Rioja wine region last Monday and you could already notice the change in the color of the leaves, it will be spectacular mid-October and November. The trees in our forests have also started changing.

There´s a direct flight from Newark Airport to Bilbao, twice a week, it does not operate all year round but you may want to check.

Of course Mikel´s comments are very solid, but I´d like to tack on a little bit.

First, for me the second half of October, from the Pilar (Oct 12th) to the Sunday we change the hour is the best time to be in La Rioja, and Rioja DOC. The days are still a bit long, the weather is usually pleasant, and the countryside is alive in color. As Mikel commented, the leave are only just starting to turn at this moment.

You say "5 day road trip, along the coast and possibly returning inland", so I would differ with Mikel and say you have time to go to the Baztan valley. I am writing from Lekaroz right now. Again, the leaves here have just started to turn, but it is very beautiful all year around. There are some very nice walks around the valley. The Xorroxin Waterfall in Erratzu is a popular hike, and my favorites are going up to Gorramendi and visiting Izpegi pass and having lunch and enjoying the view.

Laguardia is great, and you can´t go wrong visiting, but I find that it is the place in Rioja and La Rioja that comes the closest to suffering from "overtourism". Besides Sajazarra, I would suggest visiting Briones, Although visiting wineries is not a priority, Bodegas Lecea. Beside wine cellars that are hundreds of years old, they offer hikes and rides though the vineyards.

A road trip in the Basque country and surrounding area was our first, and still favorite, trip to Spain. You might consider a couple of nights in Hondaribbia with a stop at Chillida Leku, pinxtos at Bar Gran Sol, a daytrip to the French Basque towns of Sare (our favorite), Espellete and Ainhoia or alternately to St. Jean de Luz. Laguardia is stunning — so much so that we made a return trip there to savor it and to further explore Rioja Alavesa.

Have a wonderful trip!