Spain in June w/ 3 kids under 6 - Looking for ideal home base ASAP!

Off the top of my head, if you would like a Basque area, San Sebastian. The beach is gorgeous, lots of sandy area and quite a bit of the bay is shallow. Another place, in Andalucia, Cordoba. Cordoba is very picturesque and you could do many day trips from there. Another potential area would be Galicia, or east of there Picos de Europa National park.

Look into Logroño, it is a very family friendly town.

It is one of the most "green" cities in Spain, in that it has one of the highest square meter of park/per capita in Spain. So there are lots of parks and nature areas in the city you can easily walk to. Also there are several large public swimming pools you can buy passes too.
It could be hot, but it would be the hottest or coldest place in Spain in June.
As it is not the coast or a famous city, there will be few tourist here and in general it will be cheap than a seaside town.
Bilbao, Pamplona, Vitoria and Soria are all an hour bus ride from here, and there is a good regional bus system that can take you to smaller villages in La Rioja for day trips and picnics.

Hope that helps, sent you a PM.

I'd go with the Basque Country or Galicia, or somewhere between those regions. Choose a town or city somewhere near the coast so you avoid the dreadful heat of the interior. You might check lodging costs in San Sebastian on booking.com to see whether they fit your budget. (You might save a fair amount of money by booking directly in the end, but booking.com is a very convenient website for preliminary research to see what rates are like.)

I think San Sebastian is the most expensive town across Northern Spain (excluding Barcelona and Girona in Catalunya). The beach in San Sebastian is gorgeous, but there are of course other beaches all along the coast, so I don't think it has to be San Sebastian, which is extremely touristy. I much preferred Bilbao as a city, and it's likely to be significantly cheaper, but I don't know how convenient it would be for frequent trips to the beach.

I should warn you that the reason the Basque Country is so often recommended as a destination for summer trips (when much of Spain is deathly hot) is that it is often overcast and cool. Not every day will be beach weather, and I don't know how warm the water gets even in the middle of the summer. It could be distinctly chilly in June. That wouldn't necessarily be an issue if the kids would just be splashing around in shallow water.

If my discussion of the probably-cool weather has turned you off the north coast, you might prefer one of the towns along the east coast, between he French border and Valencia.

Weather in northern Spain is normally much cooler than in other areas of Spain, and it´s a very green and mountainous area, with beautiful landscapes and great food. It tends to rain often, but June, July, August and September are drier than the rest of the year. Temperatures are mild, not too hot, although we had extremely rare temperatures over 40º/100ºF last August and that was hard to cope with as we do not have or use AC at home, it´s not necessary for 99% of the time. Bilbao has an easy access to beaches on the metro (extremely safe, clean and efficient, and very cheap...around 50ct a ride with the transport card), half hour to Ereaga or Arrigunaga beaches in Getxo (I live half a mile from the first one). Bilbao has lots of playgrounds for kids with all kind of those artifacts kids like :), as most cities in Spain.

My two cents... obviously my turf: Catalonia.

Yet I rather images speak for themselves:

https://www.catalunya.com/en

And since you mention you have small kids, here some ideas:

https://fr.zone-secure.net/349017/1800720.pdf
https://isyourhome.catalunya.com/get-inspired/
https://www.timeout.cat/barcelona/ca/amb-nens/50-llocs-per-portar-els-nens-a-barcelona
https://www.amazon.com/Discovering-Barcelona-travel-guide-teens/dp/8461657454
https://www.escapadaambnens.com/

Climate?... you mention you're from Houston... nothing much to add then, you already "know" ;)

Enjoy!

We just came back from a tour that included Bordeaux France and Basque Spain.

Bilbao was awesome, it was clearly our favorite. San Sebastian would be great as well. You could visit Bordeaux, Biarritz, Bilbao and the Rioja wine region.

Either Barcelona-area or, in/around San Sebastian/Bilbao.

Barcelona itself has a lot of options but, you'll probably enjoy doing day trips or, finding a vacation rental along the coast. Plenty of communities up/down the coast such as Sitges, San Pol de Mar and Cadeques; kids always enjoy the beach and it's an easy attracation that doesn't involve too much planning.

The Basque region is another easy get-away that won't be as warm as Barcelona. The beachside communities remind me in someways of American coastal communities versus Mediterranean. San Sebastian is a not too big a town with spectacular food options, a fantastic aquarium for kids and two big beaches; Zarautz is very beachside lazy town I really enjoyed. Closer to the French border is Pasai Donibane which is more fishing village, and Irun which is the border town to France. Just over the border is charming Saint-Jean-de-Luz and just beyond is the resort town of Biarritz.

I did, a few years back, have 4 children 6 and under. I think either Catalunya or Basque/Rioja would be a spectacular place. If it were me, I'd want to be walking distance to a beach for the mornings dad is working Either of those areas offer that. I, too, did like Bilbao better than San Sebastian but I feel like the advantage with San Sebastian or any other of the beach cities nearby or just north in France beats Bilboa for a young family. Then in the afternoons and weekends, you would be close to so many day trip opportunities. For the Basque region, you'd have the picturesque French Basque villages, Rioja, Bilbao, Logrono, Biaritz, etc. There are similar opportunities in Catalunya.