I'm an NYU junior studying politics, development, and Spanish. So far I have spent one complete semester at NYU Madrid and have just started my second. In my experience, the academics at this campus have been exceptional. First, the class size is usually less than 15 - I have had one class with about 20 students, but this was by far one of the most popular on campus. The small class size allows you to get to know the professors and other students much better than in some large classes at main campus. This is especially helpful if your professors are Spaniards, since they can help you with the city and culture. There is a large range of classes here: Spanish history and culture, business, human rights and international law, urban studies, migration studies, and more. My top class so far has been Migrations & Cultural Diversity. I have been surprised by the quality of the classes here; they've been my favorite of my time as an undergraduate. Many require some form of research about/in the city, which helps you get to know the culture. The student life and academic support staff are as a whole very knowledgeable and helpful, especially with navigating classes and the new city. They also can connect you easily with medical help (including some great mental health options) and have a network of professionals in many fields.
NYU Madrid offers two housing options: a student residence and a homestay. I spent my first semester in the residence, which is centrally located in the Malasana neighborhood, very safe, modern, clean, and has a rooftop area with seats/tables/ping pong. The guest policy is pretty strict, but overall it's a good place to live. I don't have personal experience with a homestay, but all of my friends in homestays have had positive experiences. The only complaints are that some have curfews at night, and many have conservative/traditional hosts.
The city itself is a great place to spend a semester. Madrid's nightlife has a big reputation, and it lives up to it, if that's what you're interested in. There's also great bars, concert venues, museums, and cafés for more relaxed options. The public transit is incredible, so much better than New York. Twenty euros a month gets you access to the subway (which is fast, on time, and clean) and the bus system (same), as well as the light rail network which can bring you to towns as far as an hour away from Madrid. Great for day trips. My advice would be to take advantage of the transit system and go to new neighborhoods/towns as often as possible. It is as a whole safe, but some students (including friends of mine) have had things such as phones and laptops stolen from bars and public transportation. Americans are targets in any city, so be careful to keep your things close. Some of my POC friends have had troubles with racist remarks, stares, and other disrespectful behavior from Spaniards. It's a much less diverse city than New York.
If you're interested in interning, Madrid is a pretty accessible city for that. There are many agencies that help American students find internship placements, and work culture as a whole here is pretty relaxed and welcoming. I'll be interning and doing research at an organization of/for LGBTI refugees this semester, a placement I found through an agency.
Overall I'd recommend this program to anyone who wants to get better at their Spanish, live in a city that's of and connected to Europe as a whole, and study in a country with a really unique and fascinating history.