#1 Travel fitness is about maintenance, not progression
I travel to Australia frequently so I have to deal with time zones and jet lag a lot. The key for me is to get outside and exercise as soon as possible on arrival. That's a sure fire way to reset my internal clock. You don't need a gym - in fact, being inside will actually extend your jet lag by delaying a number of hormonal responses to sunshine and vitamin d. So get outside and run, swim, or hike. Remember long trips away are not about accelerating your fitness, they're about maintaining it and not going backwards. So don’t expect to push yourself like you do back home, that’s a recipe for injury. And remember, you’re probably coming off a stressful work environment and your immune system is already compromised - so don’t expect to charge hard like you do back home - that will just have you laid up sick for the trip when your immune system also decides to take a break!
My other frequent trip is to New York City where I have a bunch of business interests. Key for me on these trips is to walk as much as I can. If my meeting is 20 blocks I'll skip the subway and power walk it. Add it all up over the day and it's a lot of miles. I'll also research local boxing gyms before I travel. That's the best way to get an all round workout on the road. Again, travel is all about "maintaining" fitness, not improving it - so take it (relatively) easy.
#2 Finding a place to train is easy - look outside
I never go to gyms. I train outside as much as I can as most of my training is focused around Spartan and obstacle course racing. So I'll try to find a park or a beach and build a workout around "natures gym".
No matter where you are in the world you always have the only piece of equipment you need - your body. There are dozens of strength, mobility, and endurance exercises you can do with your body weight from push ups to lunges, to crawling and bench jumps. If I know I'm going to be near a beach I'll pack an empty $2.00 sandbag with me when I travel. I'll fill it up with sand or dirt when I get to my destination and that's my fitness equipment for the week. I use it for shoulder press, lunges, and a bunch of other exercises. And when I leave I just empty it and dump the bag.
#3 Nutrition, nutrition, nutrition
Travel means airports and airports mean fast, processed food - you just can't avoid it. So be super conscious about what you eat and drink when you are on the road. Remember if you aren't exercising AND you're eating badly (and having a few wines every night which can affect your testosterone and HGH) then that's a double (or triple) whammy against your health and fitness. I fast regularly so I'm able to go without eating for long periods which gets me past the lure of the airport food stalls. Just don't use the lack of food choices as an excuse to fall into bad habits. There's usually something (relatively) healthy (and low-carb) at airports - you just have to look for it.