Truly alien worlds shouldn't be so bad. The thing that may save character is the fact that crossing species barrier for pathogens can be hard, really hard. Think this way - have you ever freaked out about contracting virus that is wreaking havoc among your plants? Well, if yes, then something like this technically must have happened millions years ago as to virus family of Rhabdoviridae - among this family there are viruses that attack plants but also the virus that causes rabies. But for practical purposes, alien viruses should be incompatible enough and one should be worried more about bacteria and fungi like organism. (by occasion, other bigger parasites in style of tapeworm would be risky, as they would not be good at keeping their new hosts alive)
Another not so bad safe place, would be modern civilisations. The last big epidemic that brought civilised countries to their knees, was Spanish flu, almost exactly a century ago. Right now, in spite of heroic conservationist efforts of anti-vax movement, we're slowly driving most annoying viruses to extinction.
As previous places may be relatively safe (It's risky and lack of hazmat suit is recklessness, but not necessary suicidal), there is one that's bring new levels of risk. Any standard fantasy world, it's simply perfect:
- high population concentration to maintain epidemic, poor sanitary conditions
- different races (elves, dwarves, orcs...) that may serve as hosts of pathogens, but suffer no ill effects
- plenty of domesticated animals sharing living conditions with humans (including some fantastic creatures, which also may have shared their pathogens)
- hosts are similar enough that pathogens would already be compatible
(something in this style already happened in RL, that's how the most of native Americans got killed)
Honestly? After a bunch of kids visited Narnia, the Great Britain should have suffered more plague victims than caused by German air raids.
Hint: Ask questions in a bit more specific manner.