Obviously, the concensus is "bring the camera." I have the iPhone 6s and used it for quite a few photos on our trip to Italy last year, and it gives surprisingly good results in perfect conditions. The HD video is pretty amazing, again in good light. That said, photography is important enough to me that I won't rely on just the phone. It's especially inadequate in any kind of lower-light situations or when trying to capture anything where subjects are in motion. Zooming even a little bit degrades image quality in a hurry. I have an entry-level Nikon DSLR that gives fine results, but I just couldn't bring myself to lug the weight around Europe. So I got the Nikon P530 bridge camera that I've taken on our two trips abroad. While better than the iPhone, it also has its limitations -- it tends to blow out in bright light -- though I've gotten some wonderful photos with it, and the zoom capabilities are tremendous.
I'm settled now on getting one of the large-sensor "pocket" cameras, smaller than the bridge compact I have now, but with superior optics and image quality. Sony is the clear leader in this class, but they are pricey -- up to $1,000 or so. I'd even be willing to pay that, but I'll never buy another Sony product because of a long-ago dispute with the company. Long story, but yeah, I'll hold a grudge for the rest of my life. So I'm looking at one of the similar Panasonic Lumix cameras, in particular the LX100. I've got it in my Amazon cart and just waiting to pull the trigger nearer our next trip.
Here's a recent forum discussion started by steves_8 which made me take a closer look at the LX100.
https://community.ricksteves.com/travel-forum/tech-tips/holiday-photography-conundrum