While it is a good idea to complete general education requirements abroad if you can, you are encouraged to prioritize your academic interests and preference for a specific host country when choosing a study abroad program. (In other words, don’t organize your study abroad experience around fulfilling gen-eds, if you can avoid it.) For information about study abroad programs relevant to your academic interests, check out the Major Advising Page  corresponding with your major and/or consult with a faculty advisor in your department.
Also note that not every course you take abroad needs to fulfill a specific academic requirement. You can earn elective credit while abroad, too.
Finally, keep in mind that the General Education Program was designed holistically. Many gen-ed courses at the U of I are designed as continuations of one another (e.g. Western Civilization I, II, and III) and/or as prerequisites to major requirements. If you take too many general education requirements abroad, you might miss out on this continuity.