I've flown to different countries with the drone as a carry-on. I've driven across borders without issues. Drones are fairly common through Airports, and most countries with high tourism rates are used to seeing them.
As you mentioned in your comments, Research drone laws in the country/state/city you plan to visit. Your mileage may vary, but knowing laws specific to the country you would like to visit can be helpful in avoiding potential conflict. For example, in one country I visited, the maximum flight ceiling was lower than in my country. Knowing that ahead of time was helpful.
You should also be aware that in some countries (like the U.S.) laws can vary state to state, or city to city. Some cities have "No flying" ordinances anywhere in the city. You may also wish to consider that the drone hobby is often misunderstood, so even in "legal" places to fly, you may be harassed by civilians, security, or law enforcement. Always be polite, even if yo believe you are in the right. You should be especially cautious around sensitive cultural landmarks.
Some folks might prefer the "better to get caught than ask permission" philosophy, but If I'm not sure, I will just ask. Depending on who is in charge, they may give you permission to fly, even if it wouldn't technically be legal to do so otherwise...or at least allow you to fly with some restrictions. For example, I was at a state beach in another state, and was a VERY new pilot (I just bought my drone the day before). I was fairly sure the beach I was at was not a legal place to fly, but I asked the lifeguard in the area, and he told me it was fine.