Same state, same habit of having my bottle with me. I usually bring an aluminum Kleen Kanteen to Europe, but a Nalgene or bicycle bottle, or any other type works. Having a big enough mouth on the bottle for easy filling is helpful, as is a cap that doesn’t require too much fiddling to remove and reseal.
Each of the past 2 years in Italy, I had a compact The North Face pack that either my husband or I carried, with our bottles inside. No problems taking the pack and the bottles into churches - even those that had x-ray screening at the entrance, which were few.
Some museums didn’t permit backpacks, and a bag check was provided. Sometimes the bottle stayed with the checked bag, but I was able to keep my bottle sometimes - ask at the museum. Unlike airplane security, there’s not any requirement for bottles to be empty (or 3oz. or smaller!), unless they just don’t let you go thru the exhibits with any bottle, in which case you can just check the full bottle when you check the pack.
A couple more things - the more I stay hydrated, the more I need a bathroom break, and bathrooms aren’t always immediately available, so I’m not constantly chugging down more water. Sometimes you need to buy something at a cafe or restaurant to be able to use their WC/toilet, and you could’ve arguably gotten a beverage from them right there, But of course, that’s not the point of having your own bottle, with “free” water. And I’m guessing you’re trying to avoid buying one bottled water after another after another. Just never pass up a chance to pee, and never pass up having a chance to refill your bottle. A bottle that’s too big, though, is too heavy to haul around all day. Enjoy your trip!
