In reply to pantoum:
Step 1) Use Google Maps to look at mountainous areas and the nearest a hospital
Step 2) Email them and ask to come
But seriously it depends a lot on what else you are looking for. I can suggest some of the following specifics:
Kilembe Mines Hospital is at the foot of the Rwenzori Mountains - I worked there fore a month a couple of years ago and could send you the email for the medical director if you are interested. I know they take elective students. That would also give you some experience of fairly-rural African medicine. The Rwenzori Mountains take about 10 days to climb - only problem is that there aren't other mountains once they're done.
New Zealand is another good, but very different, choice. Lots of hospitals take elective students and many are near some excellent mountains. More competitive for elective placements though. I did my elective on the North Island at Taranaki Base Hospital (Mt Taranaki is a cool walk but is only a day trip!) but the bigger mountains are on the South Island. Not exactly an expedition venue but some fun climbing / mountaineering / hiking.
The IPPG rescue post at Machermo in Nepal takes elective students. Again it is competitive but potentially worth it and would give you some great experience treating altitude illness. Your dates would need to match one of their seasons. Take a look at
http://www.ippg.net/machermo-porter-shelter-rescue-post/
