I've sat next to 11 years olds in bars in San Sebastian. No problem.

I wish I knew the answer to your question about Sundays and Monday, and I hope somebody sees your post who knows, but I wanted to encourage you to take your son to the small old amusement park at the top of Monte Igueldo if weather permits. You take a 5-minute funicular ride up there. You've got to prepare your son for the fact that it is mainly a kiddie park, so he doesn't expect any modern rides or take seeing so many toddlers as an insult. But it is actually so old fashioned, it is funny, and there are bumper cars there he might like. That would make me want to go on a Sunday, but maybe he really does want to try as many pintxos as possible, and I don't know if Monday is better for that.

You know, you can also get plenty of pintxos in Bilbao. Lots of highly regarded bars. Do some google searches.

This website takes forever to load, but it shows you pictures of the park

http://www.monteigueldo.es/atracciones/galeria.html

The situation is the same in San Sebastian-Donostia as it is in Bilbao, very few restaurants will be open for dinner on Sunday and even fewer for lunch and dinner on Monday, but a few pintxos bars will be open both days, you just have to know where to look.

An no, the weather isn't the same as in the EU, more like being in Vancouver, BC or Settle in the Pacific Northwest.

Going for pintxos Sunday at lunchtime is a highlight of the week in both Bilbao and San Sebastián.

Kids are everywhere at all times, no restrictions at the pintxos bars/ restaurants.

All about going for pintxos in absolutely food crazy San Sebastián, suggested routes etc. http://www.todopintxos.com/home/home.php?lang=en

Several of my favourite restaurants are open on Sunday night:
Traditional, family-owned and affordable La Cueva: http://www.restaurantelacueva.org/index_ingles.htm
La Cepa is an institution in town and serves the best jamón ibérico (cured ham) in the world: http://www.barlacepa.com/en/index.html
Casa Vallés, just behind the cathedral, has got tons of atmosphere and serves excellent grilled meat and fish and other goodies. Fantastic jamón here also (in fact, most of the bars in San Sebastián serves ham from the town Jabugo in the Huelva province in Andalucía, as good as it gets): http://www.barvalles.com/

For fine dining without getting ruined, I can highly recommend Restaurante La Muralla. http://www.restaurantelamuralla.com/
Reviews: http://www.tripadvisor.com/Restaurant_Review-g187457-d989175-Reviews-La_Muralla-San_Sebastian_Donostia_Guipuzcoa_Province_Basque_Country.html

Past sixteen years weather statistics for the last week of October in San Sebastián says 58-72F, average four hours sun pr day and two days with rainfall pr. week.

About San Sebastián in New York Times: http://travel.nytimes.com/2011/08/07/travel/36-hours-in-san-sebastin-spain.html?_r=0

And be aware that Bilbao and San Sebastián are extremely different cities, both fantastic in their own ways. Bilbao is 10 km inland and lots of industrial history, great museums and a genuine, vibrant city feeling. Seaside and Belle Epoque San Sebastián has been a favourite summer destination for Spanish and French elites since the mid 19th century, some of the finest city beaches in Europe and of course the culinary capital of Spain if not all of Europe (fantastic food in Bilbao as well, but the very soul of San Sebastián is all about food).

"Everybody" will be out in the beautiful Parte vieja/Old town of San Sebastián eating pintxos at lunchtime Sunday. And remember to ask for the warm house specialities prepared directly on order. These also cost only some 2-3€: http://www.youtube.com/watch?v=qBhJPq-nfBE

And in the region in general, you should try the local crisp dry and slightly bubbly white wine txakolí: http://en.wikipedia.org/wiki/Txakoli

And I can highly recommend finish off any meal up here with a Pacharán/Patxaran: http://en.wikipedia.org/wiki/Patxaran

ttt

Sunday evening will be slow in both San Sebastian and Bilbao. However, I think San Sebastian has more open on Sunday vs Bilbao. I was in San Sebastian just last Sunday and there were plenty of pintxos bars open in the evening, even some of the more popular ones. Two weeks prior I was in Bilbao on Sunday evening and it was much quieter - most places closed but there were some places open.

I haven't visited San Sebastian on a Monday in years so can't help much but it is traditionally a day that many places are closed. When I was in Bilbao 3 weeks ago on a Monday there weree more places open than on Sunday evening but several pintxos bars were closed.

No problem or issue with a child having pintxos in a bar. It's not the same type of "bar" atmosphere or culture as in the US where the primary focus is generally on drinking.

The main reason why I asked whether to go to San Sebastian on a Sunday was because I thought museums like the Guggenheim will be closed on a Sunday. However, I have just checked the website, and it is opened Tue-Sun.

Reading some of the earlier posts, I was contemplating of going to San Sebastian on a Saturday instead. The rationale being that as we are staying in Bilbao, we will have more than ample chance of experiencing pintxos on the Friday evening when we arrive.

La Bretxa, shopping centre with a large traditional food market will be closed on a Sunday. Similarly, Mercado de San Martín is also closed on a Sunday. Are these 2 places worth going? If not, after reading CathyM's reply, I think depending on the weather forecast we will decide whether to go to San Sebastian on a Saturday or Sunday.

Once again, thank you everyone for your replies.

I liked both La Bretxa and San San Martín food markets better before when they were more "raw". After the total renovations they are both more like what you can find in other places with other kinds of shops, cafés, bars etc, but both contain of course fabulous food markets in the food capital of Spain.

So I think they both are well worth a visit. My old Charcutería in San Martín is still going strong. Maribel has got fantastic produce and came strongly recommended to me by my professor at the university in the mid 90's. I always bring back some Jamón de Jabugo from here, the finest in the world and very expensive. The Paleta/paletilla piece of the ham which they also use to have here is much more affordable, and I think it's just as delicious.
http://www.msanmartin.es/msanmartin/de/charcuteria-maribel.asp?nombre=2714&cod=2714&sesion=1

Would strongly recommend a whole (Satur)day in San Sebastián, allowing for (1) a food market excursion, (2) a pintxos bar round at lunch-time, (3) a funicular ride and fun fair experience up at Monte Igueldo, (4) an early evening paseo/walk along the beautiful La Concha beach promenade with perhaps a glass or cup of something at old world Café de la Concha with the best views of the beach, the bay and the small Santa Clara island, (5) an appetizer in one of the many cafés or pintxos bars with terraces in atmospheric Plaza de la Constitución in the middle of the Parte vieja/Old town and (6) a sit down meal in the evening.

The last PESA bus to Bilbao leaves at 10pm and could be combined with a dinner at 8. Taxi would be some 80-90€.