How do the locals treat American study abroad students?

It really depends on location. I studied in Dublin, for example, where everyone is extremely accepting of Americans. I found tons of people who loved to talk to American students about anything and everything — American, Irish, or otherwise.
When I visited Paris, however, I definitely did not feel the same sort of open atmosphere. This may have been because my role in Paris was tourist rather than student, but I felt a lot more judged on the basis of my being American and thus lacking.

It definitely depends on where you are. I studied in Florence, Italy and it seemed like it was half half. A lot of Italians were super nice and welcoming, and some weren't as much. If they know you're American they might charge you more for something, or give you different treatments. In my opinion, though, some other Americans who were there as well would be extremely loud and somewhat acted disrespectful which is why they were treated differently. While I was there I would be with my group of friends acting respectful and having fun but we're still treated lower than we expected. So it really could go either way

I agree with the two previous comments that it does mostly depend on where you are. Cultures are different all across Europe - some very accepting of foreigners and some not at all. But in my experience when I studied in France, and while traveling in Europe in general, I found that no matter my language ability, if I was polite and made an effort to assimilate more to their culture, rather than force my own upon them, people were really willing to help when we needed it and very welcoming. I guess it all comes down to you and anyone you're traveling with to know that as long as you respect that foreign culture and put forth some effort to try the language or eat their food or anything else, people will be very welcoming.

I also agree that it depends, both on the location and on the person. In any culture, there will be rude people. However, in my experience in southern France, locals were accepting of American students. When Americans were loud, disrespectful, or broke certain unspoken norms, then they could potentially be treated more poorly. But I had a number of very positive experiences with locals, for example a woman who worked in a boulangerie (bakery) that I regularly went to was really eager to improve her English and was very kind to me as I practiced my French with her. I've also had a store owner reprimand me for asking to use their bathroom (it was an emergency!) without buying anything. So you can easily experience both.

I studied in Milan, Italy and the locals were super excited when they found out I was from America. Pretty much everyone I met wanted to talk to me about places they had been in America or their dreams of one day visiting. I think they had this mindset because most people on my study abroad program tried to adapt to their culture and blend in rather than trying to stand out as Americans. When visiting other countries and cities, I would say it was mostly a similar vibe, but if you and your group are blatantly trying to stick out as Americans, then people will not be too pleased.

I found that I was treated very well as an American while living abroad in Spain, Costa Rica and Australia. However, there is a lot of media coverage about the United States overseas, so I was often asked questions (sometimes uncomfortable questions) about life in the United States. Gun control and Donald Trump are two topics that came up often (that I would have preferred not to have been asked about).