I've been voluntarily admitted to inpatient care several times, although none were at a private hospital. Others have already mentioned most of the things I would suggest, but here's something I don't think anyone mentioned yet.
It may work differently where you are going, but I always found it very helpful to pack some tea (bags for easy use) and a few smaller snacks in case I crave something sweet. They usually provide coffee/tea, but it can be a bit bland. For example, I always bring chai tea because that's not something they provide. Likewise, if I'm really craving my favourite chocolate, it's such a relief to already have it at hand. It requires some self-control to not eat it all at once, but you know best what you can handle. Obviously only bring a little for emergency use.
Something I did not think of my first time was that any kind of glass container is not allowed. My deodorant was taken away because it was glass and I had to ask for it every time I needed to use it. Rules regarding this probably differs from place to place, but it was just something I had completely overlooked because it's not very obvious. At one place, they took my bra because of the wires, so after that I only used wireless bras.
As for things to do, all I can say is; make use of the staff as much as you can. Don't be afraid to ask for help, don't be afraid to ask for things you need, food or anything else on off hours, and never feel like you are in the way or being bothersome. Make the most out of your time there. Hell, ask the staff to do activities with you if you want. I did hours of jigsaw puzzles with my favourite nurse whenever she had time to sit with me. Talk to them a lot.
When it comes to other patients, it's up to you how much you want to interact with them. I chose not to because on my very first inpatient stay, I noticed I soaked up all the shit others were carrying and it made me feel worse. Beyond friendly greetings and courtesy at mealtime, I did not talk to anyone who didn't work there after that. It's very individual, but try to be conscious of how you're affected by the others there and you'll be fine.
Sorry for the long reply. Hope you get something useful out of it. Good luck with everything