Santander, short visit

You should rent a car since there's quite a few interesting things to see within an hour's drive of Santander. I travel to Santander for business. My clients (who live and grew up in Santander) have taken me to the following places, so I'm passing these along to you since I assume these are things the locals view as good things to see around Santander:

1) Small town of Comillas... see the Gaudi House and have lunch at "La Aldea" (the pulpo and manos de cerdo were fantastic).
2) Small town of Santillana del Mar (see the 11th century church)
In Santander . . .
3) Visit the Palacio de la Magdalena, walk it's grounds. It's where the king & queen of Spain would go to escape Madrid's summer heat.
4) Walking west from Palacio de la Magdalena, walk along Sardinero Beach and up the bluff for great views looking back toward Palacio de la Magdalena. Continue bluff-top walk to the lighthouse (el Faro).
5) A short drive over to the small picturesque village of La Maruca on a small harbor/inlet with fishing boats moored (highly recommend lunch at "el Refugio del Pescador" overlooking the small harbor . . . must try the rabas).

For best views and location, I highly recommend el Gran Hotel Sardinero. It's on the beach. I do not recommend staying "downtown" or on the main harbor area of Santander.

Because of a catastrophic fire in the 1940s, Santander has few significant buildings over 75 years old. Its main tourist attractions are the beautiful beaches. I'd spend my time outside the city. A car would be really helpful, though it is possible to get to both Comillas and Santillana del Mar via public transportation.

In addition to the suggestions you've already received, I want to mention the Picos de Europa area. Some guidebooks call its scenery the prettiest in Spain. I was limited to the spots my bus-tour took me and highly recommend the beautiful old stone town of Potes, but there are many lovely areas--both mountains and gorges.

Near Santillana del Mar are the Altamira Caves with prehistoric art. I think they require pre-booking.

I haven't been to Santander. But I see from Rome2Rio that it's less than 1.5 hours to drive from there to Bilbao, which I very much enjoyed. There's several great museums (not just the Guggenheim, but also the Bellas Artes and the Museum of Reproductions), a very interesting old town with unusual shops, and a dynamic vibe for a city of its size.

This is wonderful information - thank you. I'm super excited.

Do you have recommendations on where to stay -- We will be in Santander for 2 day's, then we have a chance to travel for 2 day's - would you recommend going to San Sebastian

Many love San Sebastian; I preferred Bilbao. There are also the small Basque beach towns like Getaria, Hondarribia, Zarautz, and Lekeitio. It depends on what you're looking for.

Here's what I wrote about San Sebastian vs. Bilbao on another thread:

"They're quite different, so which to keep and which to drop is up to you. San Sebastian has few "turnstile attractions" other than the aquarium, but it's lovely and a nice place to hang out. Bilbao is a much larger city with a real urban feel, several good museums (the Bellas Artes and the Museum of Reproductions in addition to the Guggenheim), and a more interesting Old Town than San Sebastian, including a much larger market. I much preferred Bilbao, but if your goal is beaches, beauty, and relaxing, pick San Sebastian; Bilbao is definitely a bit "rougher" and less pretty."

If you really want all my impressions of my Basque country trip (warning - it's long): https://community.ricksteves.com/travel-forum/trip-reports/basque-country-trip-report-bayonne-san-sebastian-vitoria-gasteiz-and-bilbao-may-2017

For what it's worth, I'm with Harold. The super-crowded tapas bar scene in SS just wasn't for me. Probably being a non-drinking solo traveler was a big factor there. If you are convivial sorts and not particularly interested in art, SS may be more your style.