What is the best work travel advice you’ve ever been given?

It depends on where you're traveling.
International travel outside of the U.S. almost always has some sort of unique flavor that needs to be accounted for.  
Probably the best advice I received is related to making assumptions about the infrastructure of the country you're visiting and it's 3-fold. (could be 4 depending on how you choose to lump and split them)
1-Don't assume the water is safe for consumption.
2-Never forget that also means no ice in your beverage.
3-Drink bottled water and always open it yourself because you want to avoid a bottle that has been refilled.

Some things are just so simple they escape us.

1. Never check a bag. If it doesn't fit in carry on - you don't need it.
2. Timeshifter app to minimise jet lag
3. Rehydration tabs during long haul travel
4. Really - never check a bag

Stick with one airline (or alliance) when possible. Status and miles/points will be helpful one day.

The extra 30 dollars for the exit row seat is always worth it, and never ask a taxi driver or hotel employee where to eat. Ask a local. 

1. Bring a backup cell phone. You can always download a SIM via WIFI
2. Plan your lounges from airport to airport
3. Use the app - Timeshifter to mitigate Jetlag.  It works great!
4. Bring one change of clothes in your carry-on, just in case your checked bag is delayed or lost