I was fortunate to get to go overseas four times as a cadet, all in different programs. Here is what I got to do...
Operation: Air Force: I went to Spangdahlem AB, Germany for three weeks in the summer between my 3* and 2* years. This was the standard "ops" program that everyone went through, and I shadowed OSI, JAG, and comm. They gave us three or four day weekends both weekends that we were there, and I was able to take the train to Luxembourg, Belgium, and Holland in my free time. We didn't get to put preferences at that time, but as a general trend it seemed like the "better" bases went to people with higher class ranks. I didn't have cell service for this trip and never needed it.
Olmstead Foundation Cultural Immersion Trip: I got the chance to go to Vietnam, Cambodia, and Thailand over two weeks in the summer between my 2* and Firstie years. Getting selected for a trip like this was totally dependent on making a relationship with an instructor that was planning on putting in an application with the academic department and the Olmstead Foundation for funding for a trip. After a trip to Africa had fallen through the previous summer, a professor in the Poli Sci department was able to work this one out for a group of four of us that he had taught during our 3* years. It was basically a tourist trip, and we went with 2 AFROTC cadets, USMA cadets and USNA midshipmen. I think I had international service on my cell phone for this trip, but I always used internet cafes instead. My phone was stolen out of my luggage in Cambodia, so I definitely didn't use it after that!
Deployed Ops: I applied and was selected for Deployed Ops the summer between my 2* and Firstie years as well. Between that trip and my Olmstead trip I had a grand total of 5 days of leave that summer, but it was definitely worth it. I knew I was going to be a contracting officer, and I spent 21 days with the Expeditionary Contracting Squadron at Ali Al Salem AB, Kuwait. The other 11 days of the trip were spent traveling or waiting for airlift at Al Udeid AB, Qatar. This trip was an unbelievable experience, as I actually got to work directly supporting the base and troops in Iraq. We were there long enough that everyone earned the Global War on Terror Expeditionary Service Medal, and that month was definitely one of the most rewarding experiences that I've had in my 4 years as a cadet or my 5 years of active duty time. There were plenty of morale phones on base and I definitely didn't need cell service.
Spring Break Language Immersion: I spent spring break of my Firstie year at the Escuela Militar de Aeronáutica in Uruguay, or the Uruguayan Air Force Academy. An email came out at some point in the school year asking for applications for Thanksgiving and Spring Break language trips. I had taken two years of Spanish, but I wasn't even in a Spanish class at the time that I got to go on the trip. Four cadets were selected and the Uruguayans basically treated us like royalty. We stayed in their dorms, and they flew us around the country in their Air Force's planes. We went to the beach, a "discoteca," and ate a lot of great food. We also got to take two "day trips" in Buenos Aires, Argentina when we had long layovers and I think it was one of my favorite major cities that I have seen around the world. I didn't even think about my cell phone on this trip.
That was probably way too long, but the overseas opportunities were one of the best things about USAFA for me and I love talking about all the places that I got to go!