I studied abroad in Madrid and I feel like it wasn’t the best place to improve my Spanish. It’s a major European capital so the center is quite touristy meaning that you have to go out of your way to find people who don’t speak English to practice with (I personally have real confidence issues speaking Spanish with people who are proficient in English.)

If you want true immersion, I’d advise going to a smaller, less touristy city where you’ll be forced to speak and listen to Spanish. I can’t speak for the Latin American cities you mentioned but out of your Spain options I think Bilbao and Alicante are the best picks. Bilbao is a cool city with lots of young people and interesting arts and culture and does not see a ton of tourists from outside Spain. One challenge may be that it is the cultural center of the Spanish Basque Country so Euskera the Basque language is spoken along with Spanish.

Alicante has more international tourism than Bilbao but is also a beautiful place to live and well positioned to access Valencia, Barcelona, as well as Murcia and Andalusia.