As dubfan says, you really want a bridge camera, pretty much all PAS camera these days, let you change the aperture, shutter speed, and ISO the same as you would on a DSLR (not with the same range though) the only other item you're going to need control over is the white balance.
Personally I wouldn't touch fuji as there colour balance is generally shocking, of the top of my head i'd be going for the powershot G11 or the Nikon P100, these are both in the entry level DSLR price bracket though, but with versitile glass.
The important points to consider would be, what batteries? If it uses a bespoke battery, can you charge it in your hotel? Memory, what sort, and can you transfer images off during the trip as you'll probably fill up your cards quite quickly, lastly how robust does it need to be? when's the monsoon season are you heading to the beach etc?
What you looking at budget wise, as you could be happy with a coolpix or a powershot is
