Professional road warrior here who gained 13 lbs within the first year.
When I'm traveling I eat a salad a day. Notice I didn't say "try to eat". Sometimes it is lunch and sometimes it is dinner, but I always get a salad a day (no cheese, light dressing, tons of veg).
It can be tempting to hit some of the more fancier restaurants because someone else is paying, but after a while, all the menus start to look alike. For me, I've found that going to one nice dinner a week satisfied my craving for a higher end meal. For the other days, I hit the grocery store and stock up on fruits and veggies to keep in my room.
As far as working out, I suck at this. I'm inconsistent, but I found I worked out best in my hotel room. I have several Beachbody* videos (Insanity, P90X3, PiYo, TurboFire) that I ripped to MP3. I love these because the majority can be done using your own body weight and you get a fantastic work out. I keep these on my laptop and just pick and choose.
*I am not a Beachbody rep, I just like their workouts.