I'd probably start by working intensely for a while to finance going to these places. I'd love to work in a hospital in Zimbabwe, but first I'd need some kind of helpful skillset, so I might start by getting a phlebotomy certificate and learning to perform basic lab tests. Ideally, I'd complete this before graduating so I could jump right in.
If I were staying in one place, this could be a mission trip, but with so much moving around, it's difficult to contribute much. One way to solve this problem would be to do HIV education/basic health education in rural villages. I'd need a translator for most of these places, but if I could find hospitals with someone to spare, this would work well. I would start by spending time traveling around Africa, starting in Zimbabwe, spending a bit of time in Harare, Gweru, and Bulawayo (my mom and grandparents spent time in all of these places). I'd also probably travel around rural Zimbabwe a fair amount, and spend some time in Uganda and Nairobi, Kenya. If I could scrape up the money, I'd also love to travel to Brussels, Italy, and the U.K. But I'd much rather travel with someone else for these; it's better to have an awesome experience with someone else if the trip itself doesn't have a purpose. Anyplace that has internet, I could tutor to help pay for transport, but airline fare would be pretty expensive and probably not affordable by this plan. I love traveling, but moving around for a year would make it hard to develop relationships and I think it would get lonely. If there were a way to fund it, I would go, but given the choice, I might wait. Traveling is a wonderful thing to do if you can, so if I got this opportunity, I don't think I would regret it. Understanding different cultures and meeting different people is an exciting and enriching experience.
Really though, I'd love to do something like this after I graduate from residency or fellowship because there would be more I could learn and more help I could provide. Working in a hospital with fewer resources provides a totally different perspective on healthcare, global health, and diagnosis, and I would love to be useful. Maybe before I retire I'll be a cruise ship doctor for a year or two (if cruises survive this fiasco) or work for Samaritan's Purse/ Doctors with Borders.