I travel quite often for work, and it was my downfall several times. I've made it through a few week-long trips sober, and trust me, it feels so much better traveling while not hungover.
First off, PLAN ahead. Bring workout clothes and plan to get up early and go to the gym. Even if all you do is walk the treadmill, just plan for it.
Order a non-alcoholic drink right away, so that you don't have that empty hand. If someone asks if you want alcohol, just say up front "I don't drink." Most people will drop the subject immediately because either that answer was enough for them, or they just don't care enough to dig deeper into your meaning behind that answer.
Finally, if everyone else is drinking, you're not missing out on anything...instead, you now have the upper hand by remaining sober and clear headed. You'll really be able to read people, and maybe even take some mental notes you can use in the future. And continue to tell yourself this "I won't feel awful tomorrow morning"...that helped me so much, knowing I was going to be at the gym, clear headed, and taking on the day, instead of hungover.
Just some thoughts. Hope it goes well.