There are about a billion and one opinions on which workout program is the best. Should you run? Should you lift weights? Should you swing your legs gaily on a Richard Simmons' Gazelle?
There's one answer that will work for pretty much everyone: Crossfit.
Crossfit is designed to be a total workout system. It addresses the 10 areas of fitness (strength, endurance, agility, flexibility, cardiovascular health, balance, and four more that I've forgotten). The end result? You get in such good shape that you can tackle any sport or activity, from basketball to mountain climbing.
Best of all, it's free. Go to Crossfit.com and do their workout of the day. Some are difficult (running 10 kilometers), some are quick fifteen minute workouts. Two or three days out of every week are rest days.
No fancy machines are needed. Just basic weights, a pullup bar, and your bodyweight. They have lists of substitutions if you can't do a certain exercise, and there are videos showing you proper form for everything.
It's also possible to do some of their exercises without any equipment at all, so you can stay in the groove while you travel. I've been personally doing Crossfit for 5 months now and couldn't possibly recommend it more highly.