One of these is the Fulbright Schuman program (https://us.fulbrightonline.org/countries/europe-and-eurasia/european-uni...), an initiative between the U.S.A., Belgium and Luxembourg aimed at increasing American scholarly interest in the E.U. on a wide variety of topics, even those not directly tied to E.U. politics. As previously mentioned, there is also a CBYX program for college students that functions a bit differently but is the same in the spirit of a U.S.-German cultural exchange.
No matter what, if you're interested in studying abroad as part of a bachelor's degree, I strongly recommend checking out the Benjamin Gilman scholarship (https://www.gilmanscholarship.org/program/program-overview/). A Department of State-sponsored initiative to get American students on Pell Grant out into the world, the Gilman Scholarship provides additional opportunities to enhance your study abroad experience. All of the pictures to the side come from the Brussels study tour that the Department of State and European External Action Service host in Belgium, and even though it was only three days, it was easily one of the major highlights I hold closely in mind. It was also a fantastic educational opportunity that, in part, contributed to this very post! Oh, and did I mention that no money comes out of your pocket for this?
While I've tried to make a somewhat comprehensive list of possibilities open to someone interested in studying German and learning in Europe, you all are individuals with your own interests and passions.