We arrive on 25th around 13h. And we are staying on Staten Island. Is there something nice to do there on Christmas Day? I guess before we get out of customs etc it will be late in the afternoon.
Where are you staying on SI?. I think the answer will depend on that and how you will be getting around. Not much will be open on Christmas Day except for some restaurants.
Staten Island is NOT a good place to stay unless you have some specific reason to be there. It is a primarily residential area and to get from where you are staying to Manhattan will probably take you about an hour - and then it may take up to another hour to get to what you want to see in Manhattan.
Unless you simply can;t afford it you should try to stay in Manhattan (where there will be a ton to do on Christmas) or else another part of the city much closer. For instance there are a bunch of budget lodgings in Long Island City that will get you to Manhattan in about 15 minutes on the subway - and you can start seeing sights immediately.
Please post where on SI you are staying?
That will assist us to answer your question.
Near latourette park and new spingville
Please note that this is a very inconvenient location for getting into Manhattan (and then back). You'd have to take a bus all the way up to the St George terminal and take a ferry to Manhattan. Probably 90 minutes from there to midtown.
That area is by the Staten Island Mall, if you wanted to shop.
As already noted, if you are planning on visiting Manhattan every day, that is not a great area for transit.
See link below for the bus map of Staten Island.
There is no subway on Staten Island. Note the difference between types of buses.
Express bus cost $6.50 per person per trip. Most buses only run to Manhattan in AM rush and to SI in PM rush.
Your original post asks what is open to do on Staten Island on Christmas Day. Unfortunately, not much. You will be staying in the most residential of all boroughs of NYC. The mall will be closed. Most restaurants will be closed and those that aren't, may have special menus.
There is a movie theatre not far from where you are staying. The Atrium movie theatre is on Arthur Kill road. Getting there by public transit will be challenging.Perhaps a car service or Uber?
Being a tourist from that locale will be a challenge.