I think saying it's like "NYC or SF" was not saying they are similar, but exactly the opposite, that it's all a matter of taste. Aside from being big cities, NYC and SF are very different. Madrid and Bilbao maybe even more so.
Madrid is the capital, of course, and has a lot of tremendous cultural sights -- the Prado Museum, the Reina Sofia, the Palacio Real; as well as the Parque del Retiro, great shopping and nightlife, Real Madrid, to mention just a handful of things. If staying around Madrid, I'd also recommend Toledo, the former capital and a beautiful smaller city 30 minutes away by train. Tons of history and spectacular views.
You could also have a tremendous trip doing Bilbao and San Sebastian (and maybe popping down to La Rioja if you want to explore wine country a bit). As mentioned above, Bilbao is more industrial. The Guggenheim by Frank Gehry is of course a highlight, and there's also tremendous food, as is true all across País Vasco. Unless it's changed, San Sebastian has more Michelin stars per capita than any other city in the world (excluding if a tiny town has one restaurant). It's also very easy on the eyes, and the coast between Bilbao and San Sebastian is lovely as well. La Rioja is not a long drive, where you could explore some vineyards. Logroño is a nice base if staying overnight, with Calle Laurel being known for its string of pintxos spots - each restaurant is known for one thing.

Based on your interests of art, food, wine, beautiful scenery, country back roads, I might pick the northern route. Art you will have more options in Madrid, but you'll get plenty of everything else in País Vasco (and La Rioja if desired).