It all depends on what you are looking for in a camera, regardless of where you are going. Do you want something light and portable? Do you plan to take a lot of indoor shots or will you be primarily shooting outdoors? Do you need something that can zoom in for wildlife viewing? How much do you want to spend?
The first camera I brought on my Alaskan cruise was a Canon Rebel T1i DSLR, for which I spent a fair bit of extra cash to upgrade the lenses. It took beautiful photos, and it does well in low light - BUT it is quite heavy, and it can be cumbersome to change the lenses out, and frankly I get tired of carrying it around on most of my trips. So, I also bought myself a Canon Powershot G7X, which is very light & compact, but also takes amazing photos, and even does fairly well in low light - not quite as well as the DSLR, but as I prefer photographing the great outdoors rather than indoor venues, it perfectly suits my needs. I took it on my next Alaskan cruise, my first caribbean cruise, and to Animal Kingdom & Animal Kingdom Lodge where I got some amazing shots. Without the zoom lens I didn't get as close up as I could have with the DSLR, but to me it was worth the trade-off not to have to lug all the big stuff around. It's definitely on the pricier side for a compact, but well worth it!
Hope this helps!
Aby