My son will be studying in France and Sweden next year through DePaul University. The University of Southern California has a very strong international program in which most students participate. It's a great opportunity to learn the culture of other countries while in school.
There are tons of study abroad programs which allow students to directly apply to a foreign university (without applying via a US college). Two such programs that I have personal experience with include:
Chinese University of Hong Kong in China
Copenhagen Business School in Denmark
Hope this helps!
Great question - definitely reach out to your campus' international studies department or academic department, they will give you the best information. I studied abroad during the Fall Semester of my Junior Year and loved the experience.
I was able to go to Florence, Italy and made sure that my classes lined up with my undergraduate requirements. If you or anyone is interested, I recommend asking questions early. I was able to take my fine arts credit while abroad - which involved going to different museums most weeks around the city - defintiely better than spending a semester learning through a textbook!
Hope you get the opportunity!