If you're American, Peace Corps is a good idea. It's a long stay overseas, but you get to see a lot and have a lot of freedom to do things you like. At the same time you are well covered by American diplomatic presence abroad, which can be an asset - when the revolution broke out here last year, the Peace Corps volunteers got shelter at the US army base, for example.
Also spending time with Peace Corps will then allow you to get a degree for very little money from good universities, and it looks very good on the resumé if you care about that sort of thing.
Outside Peace Corps, you can always try to hitch an internship with a larger organization. If you have a bit of journalism experience it helps, of course. It's always easier to do this from within the country you want to go to. I have a reasonably good job for a large German development organization in Central Asia and I wouldn't have got the job if I hadn't happened to be in the region and could have talked to the people on the ground, before sending my CV to an insensitive HR drone in some headquarters in Germany.
The most important thing in the world is knowing languages. This holds both for getting jobs and for working effectively as a journalist. In practice that could also mean that if you know a foreign language well enough, for example, to teach in that language, you can always go and teach basic photojournalism at a college in the country of your choice. Within a short time you'll get lots of offers to photograph things.
It means a lot of work for free (which is usually a bad idea), but if you can cover this under a humanitarian engagement and you are genuinely interested in what they're doing, it might be worth it - as opposed to doing internships at home, which is a waste of time and effort.
The idea of organizing a trip yourself short of booking the tickets, and then sending around a few emails that you'll be in the country and whether they would be interested is very good. My brother, who's a medic and speaks Spanish pretty well, organized himself a half-year internship in a Mexican emergency room by calling all the local divisions of the Red Cross in Mexico and asking wether they have use for a German medic who'll work for free, with no strings attached. As soon as he found one who said yes (didn't take long), he didn't contact them anymore so that they couldn't say no, organized the tickets for himself, flew there and did it, and everybody learned a lot in the process. I guess you could do a similar thing.