I'll second Greg on this certainly being feasible, but I also agree with his comment that traveling and work slows you down a lot. It's hard to be mobile and put in the hours that most of us need to keep the clients happy. And much to my surprise I found myself missing a real office, all that stuff that offices accumulate turns out to be quite useful. In fact I've taken to working from within a friend's company just to be able to have easy access to copiers, desks, meeting rooms, etc. An atmosphere of other people trying to get a day's work done has its merits too. At a minimum I need to create a mini-office wherever I go, where all my work stuff can be laid out.
Settling down in one place doesn't seem to be your goal right now, and has visa complications as well. But I'd suggest you look to places that let you stay for a period of several months (though 'visa runs' probably being required). I tired of cafe's quickly. Maybe that's just me, and others are more flexible. But if you can stay for at least a few months it will make it possible for you to rent a place to live and set up a real office space for yourself at home. This will let you unhurriedly explore your new home and get some real work done.
As for time differences, that hasn't been much of a problem for me. The occasional 3AM conference call is annoying but rare in my circumstances. Often the time difference has meant that I get sent an email request for urgent work, sent at 6PM their time, with a request pleading if could get done by the next day. Since this arrives in my early morning mail I have the whole day to work on the project, they get the completed project back in their morning mail, and I'm the hero. But if you have to talk to clients a lot, I agree with Greg that a significant time difference would be very trying.
