I never think about these things, but was thinking about this one.
I think I'd probably set aside enough to stop working for sure, and buy a few properties...places I might like to vacation, places I might like to eventually live. Honestly, I'm not at all sure I would move anytime soon. I'd set enough aside to be able to travel significantly and definitely never have to work again.
I'd want to set enough aside for my kids and future generations that they would never be at risk of financial distress, but not so much that they basically become trust fund kids or draw the worst of the worst gold-digging partners or hangers on. I would like them to have the security of knowing that say, my grandkids can go to any college they get into, or my kids could start a business and there would be backing for it, or could drop to one income when their kids are little, and that they'll never be wiped out by an illness. But I would still want them to need to live normal lives with normal responsibility.
I don't know how you set that up with limits, etc...but I'd want them to just kind of live like normal "really wealthy" people that we all know...but not like that ultra level Trump kids or Kennedys.
Then I think I would take the bulk of it and figure out one issue that a few hundred billion dollars could really legitimately make a difference in. I don't see myself just throwing it all toward cancer research or homeless charities or something, although I'm sure it would be helpful. I'd want to find something that I could "fix".
Not saying it would be this, but for example, there is a massive amount of backlog in DNA testing throughout agencies...primarily law enforcement, where there are literally criminals who walk free for a decade because the DNA doesn't go tested for years. There are unidentified bodies, and loved ones looking for missing persons, that can't be tied together because it's just not a priority to be processed. Not talking about months, but YEARS of delayed justice or answers.
It's a real problem, one that few know or care about, but something like that seems like something a few hundred million dollars could make a real dent in, between grants to create and modernize crime labs throughout more jurisdictions, and some well funded lobbying to get support for these things in state budget.
I think I'd basically want pretty much the same lifestyle as if I had won two million dollars. Much more than that, and I think you're just talking about headaches...managing foundations, tons of personnel working for you, having to shield yourself from the world. I have no interest in having to manage and protect an empire to deal with my interests. That would be worse than a real job I think.