There is no substitute for a talented and educated eye. You don't have a lot of time to work on that before you go on vacation, so you will have to make do with what you have on this trip. I suggest writing down all our major stops, going on Flickr and searching for pictures taken there. This gives you an idea of what others did, which you might want to improve on, imitate (blah) or discard. The next most important thing is to practice. Whatever you own, carry and use it every day, from now until you depart. Make lots of exposures, familiarize yourself with controls and modes, to the point that it becomes transparent.
Oskar Barnack invented the Leica because he was convalescing from tuberculosis, and a tourist in high, dry territory in the mountains. He wanted a small, pocketable camera he could take along on his walks, and created the Leica. He would have loved cellphones. If you are OK with prints around 10x10" or maybe 12x12", can live without long telephoto focal lengths, low-light performance and its other limitations, your phone might be all you need. You already own it, it weighs nothing (since you would carry it anyway), and can send pictures back to friends, facebook, instagram, etc. It also does not get in the way of enjoying times with your family. In order to get the best possible outcomes with your phone, you need to acquire serious experience with it. Before your trip, use it frequently, trying out the different modes and see the results.
I would advise getting a larger capacity battery for the trip, and at least one or three extra memory cards, plus a car charger that plugs into the cigarrette lighter (if you're going by or renting a car when you get there.
Put in some practice time and test the different metering modes as well as your flash to ascertain the maximum distance that it can reach. On location, no matter what camera you are using, make LOTS of exposures, if possible. By lots I mean 5+
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Point and shoot cameras are small, lightweight, self-contained, and more flexible than most phones.