This isn't exactly *studying* abroad, but a friend is abroad right now through this organization that has opportunities for missionary travel in E. Europe. Finishing the 2x3 Campaign | Josiah Venture
Your question is a great one to ask a study abroad adviser at whatever school you choose, who would have more ideas on where to look. One way to go about your own search would be to seek out christian schools like Pepperdine or George Fox (try the Council for Christian Colleges and Universities for more schools) and see what study abroad programs they administer or offer to their students. Many christian schools will offer study abroad programs that are aligned with their own values and mission, but as a student at a secular school, you should also be able to spend your semester abroad in a program of your choosing if you go to a school with flexible abroad policies. I realize you're still a high school student, so many of these concerns are a little further in your future. As long as you choose a college with A. specific abroad programs you're interested in, or B. flexibility in allowing students to choose or petition for programs that may not be pre-approved by the institution, you should be fine and you can put off this concern until later down the road. (though I find study abroad one of the more exciting things to research...)
It looks like this website specializes in Christian abroad programs, though I'm sure you could find additional programs through a Google search. BestSemester About
You might also consider studying abroad at non-Christian colleges in countries where faith is a salient part of existence, like Israel or Morocco. I have a very openminded, Christian friend who loved her stay in Morocco (particularly after being in France for some time), because God and worship were expected to be part of every day life and not secularized, and people enjoyed religious discourse and discussing relationships with God, regardless of the fact that her and her hosts were of a different religions.