Having lost my dual voltage travel kettle a few moves ago, I dug up my old Zelco Brisk Brew and use that as a water heater. Instead of using the filter basket, I bring disposable finum-brand filters that I can fill with either coffee or tea and drop that into the cup and let the grounds/leaves steep as the water is dropped over it. Cleanup is as easy as squeezing the excess liquid out of the bags and tossing the remains into the trash.
The coffee made from this method is sort of a cross between French press (where you let the grounds steep) and strong drip (where the paper filter absorbs some of the oils).
I'm thinking of buying a new travel kettle though as it does take a while for the safety-thermostat to reset itself in the Brisk Brew and I'm always wanting a second cup before it's ready to go again.
I tried the Aeropress, but sometimes I'm too tired, jet-lagged and uncoordinated and upend the mug I'm pressing onto myself
Besides, most of the time the problem is having access to hot water to make the beverage.