Do we need to buy tickets to visit this place? Can those who are not staying at Bellagio visit this place?
I've walked into it several times. There's no form of admission control. You do not have to be a guest there--we are locals, we have never stayed in the Bellagio.
(Just to keep this current: Sep 2018, still no access control.)
I think that everyone passing in Bellagio can visit the garden. It will be the first example of a town requiring a stay in order to visit an attraction. You can book a room in another village, town or even country (Switzerland is not that far).
For tickets more info at https://g.co/kgs/xBXhQn
Edit: this is valid for the original question ~that did not mention Las Vegas~. I am aware is of little value now as for info about tickets, opening time and so on can be easily found in internet without asking SE travel. And this independent of being the Tour Eiffel the original or a copy.