It's just a general question- you don't necessarily need to go with a camera.
I found out that I enjoy traveling quite a bit now and to some extent the camera can enhance or detract from the traveling experience.
In some cases, when you're the designated photographer, if you get a big family you get hassled by people wanting their photos taken. Or if you're traveling with a tour group or family, you may not get the time you want to photograph something. It can be inconvenient at times, but it's definitely something to consider.
If I were to go, I'd definitely be bringing my camera for sure. I'd like to go to Kyoto, Japan, France and England. Mont Saint-Michel would be a very nice place to visit.
My only issue is time- I haven't got any right now. I'm really busy with school stuff for at least the next 4 years, possibly longer. Japan can be incredibly photogenic, but I know zero Japanese, so that may be a problem.
I may not even want to go for a week or two- I'd like to stay for longer, possibly 3 to 4 weeks in just one city and wander around, sort of what I did when I went to Hong Kong. It was nice to have a home base and just wander around some streets, going where you'd like and trying out street food without a real aim.