Same as most other advice: what I normally have. Flying, I pretty much never bother. Lots of hoops. Overseas: hahahaha. But I used to do at least once a month drives, for years, so would bring then my two normal guns. Full size for beltline, and compact for the fannypack for running, etc. I am not super duper happy having one gun either in the room or the car but it's gone okay for years so whatever.
I tend to keep them in the luggage, flopped closed or otherwise concealed real well, basically in case I am super forgetful in the morning, it won't be found by housekeeping when they remove the towel from the nightstand, or whatever. I do often leave telltales; they don't normally mess with your luggage.
Hotels are not especially more poorly built than a typical office, quickiemart, house, apartment, so not sure why I'd change anything out like ammo. #4 buck was a good idea fairy thing in the 90s. I do not recall the proof but by the early 2000s it was demonstrably marginal vs OO, much less 5.56. Like picking a .380, when you don't have to.
Now I do change my training gear. Never carry airsoft and trap, for example. But I do bring the SIRT as it's quiet and as long as the shades are down, I can do stuff in the room. Often get a big enough room I can clear the place from a few different angles, doing stuff like shooting all light switches, outlets, and fixtures as targets.