It's always a good idea to stay hydrated, and an even better idea to do it with a reusable water bottle! Not everyone needs a reusable water bottle. Don't go buy one if you wont actually use it. Look at your lifestyle. Do you normally buy a lot of plastic water bottles that could be prevented with a reusable one? If you are out and about, I'm sure many food places will give you free water to fill up your water bottle if you ask, or have water fountains accessible.
Side note: my new favorite part about the Philadelphia Airport is that all their water fountains now have bottle filling stations! So much easier than awkwardly trying to fill up from a normal water fountain. Go through security with an empty water bottle and never buy over priced airport water again. :)
I prefer to only put water in my bottle to prevent tastes building up, but if you don't have a problem with it (or maybe have two bottles, one just for water) then you can always ask places with soda fountains if you can use your own bottle instead of their plastic cups. Some places might say no because they can't keep track if you actually paid (so even if they do say yes, hold onto your receipt while you are there!) but many places will probably let you. I know Panera Bread lets me use my travel mug for coffee (but travel mugs will be a different post). It never hurts to ask! Just be sure you know how many fluid ounces your bottle holds so you can pay for the appropriate amount.