Appreciation for culture in Europe is much deeper than in the United States. Art, music, history, science and architecture are celebrated and considered as a critical part of every city´s and country’s identity. That idea is clearly emphasized by the accessibility to cultural events for the average citizen. The closest I can compare it to is monuments and museums in Washington DC, where most, if not, all, attractions are free and open to the public.
Just in Madrid, there are dozens of museums, clubs, monuments and tours that are free or discounted for students and young adults. Additionally, many museums have “open access times” or a schedule describing weekly or daily hours that certain museums are free to the public (usually a donation is recommended, but not required). International Museum Day (May 18) is recognized by a large portion of museums which typically offer free admission for all.
Also in Europe, a youth card program offers an identification card that has tens of thousands of discounts available for cardholders. It costs between €5-19 depending on where it’s purchased and is well worth it. It is an option for anyone aged 14-30 and you can find out more information here: https://www.eyca.org/.
PRO TIP: if you have a student visa in Spain, you receive an Número de Identidad de Extranjero (NIE) on your visa. This number can be used as identification so you can open a bank account, access Spanish-citizen-specific discounts at some monuments/museums, etc.
Here is a quick list of museums specifically in Madrid that give discounts or free entry to students and those under 26 (both with valid ID).
Museo del Prado (Link)
Saturdays: 6pm-8pm, Sundays: 5pm-7pm
Palacio Real de Madrid (Link)
For European Union and Latin American citizens, residents, students, etc (with valid ID)
October-March, Mon-Fri: 4pm-6pm; April-September, Mon-Fri: 6pm-8pm
Museo Reina Sofía (Link)
Mon: 7pm-9pm, Wed-Sat: 7pm-9pm, Sun: 130pm-7pm
Museo Thyssen-Bornemisza (Link)
Monasterio de las Descalzas Reales y Real Monasterio de la Encarnación (Link)
Wed-Thurs: 4pm-630pm (last entrance at 530pm)
Museo Arqueológico Nacional (Link)
Sat: 2pm-8pm, Sun: 930am-3pm
Real Monasterio de El Escorial (Link)
European Union or Latin American citizens, residents, students, etc (with valid ID)
October-March, Wed-Thurs: 3pm-6pm; April-September, Wed-Thurs: 5pm-8pm
Museo Sorolla (Link)
Sat: 2pm-8pm, Sun: 10am-3pm
Museo Cerralbo (Link)
Thurs: 5pm-8pm, Sat: 2pm-3pm, Every Sunday