If you want one of the power-zoom cameras, i.e. you want to take a picture of a whale off Kauai while standing on the beach in Maui (just kidding...) the PowerShot SX40 or the Lumix FZ150 are both nice from what I hear with the Canon a bit cheaper (but the Lumix has a Leica lens, and since most of my family worked for them at some point, they are much better, of course
). But they are bigger cameras.
For something cute you can put in your pocket, the Lumix ZS15 or ZS20 look like a great travel cameras. And unless you want to see your pictures on a 84" screen or print large posters, that should be all you need. I actually prefer the ZS15 because of the maximum shutter speed of 1/4000 sec. That means that in the very bright light in Hawaii, you will get very short exposure times - less likely to overexpose your pictures.
The Canon S100, Olympus ZX-1, Lumix LX5 or 7 are one step up in picture quality, but they have less zoom to catch far-away objects and instead let you do all kinds of fancy manual things you may not have much interest in. All of those have a point and shoot program, I use a few Lumix cameras and they call it 'intelligent auto' - works like a charm. You can switch on face recognition, so the camera recognizes that there are people and automatically focuses on faces - also works great (I assume most have this now, but I know that it works really well in Panasonic cameras). Personally, I would not go for the Nikon 1 series in your case because then you would have to get different lenses and fiddle around with that.
So, if I were to recommend or give one to my Dad as a replacement (which I may do for Christmas) that requires little maintenance and is easy to handle, I would go for the Panasonic Lumix ZS15. But in the end this is like the question 'Which knife should I buy?'
My 2 cts.
Stefan