I call this "fantasy philanthropy." How would you spend a large amount of money? What organizations would you donate to? Would you spend or save most of it?
I'd donate to 3 organisations I expect to influence government decision making positively:
(1) Happier Lives Institute. When governments try to decide what projects to prioritize, they normally consider financial/health benefits. Being able to compare the wider benefits to people's wellbeing would be a powerful new tool.
(2) Centre for Women's Justice. I don't know of any country that competently prosecutes domestic violence and sex crimes. The Centre for Women's Justice is strategically prosecuting specific government decisions in order to set new precedents for women seeking justice.
(3) The Simon Institute for Longterm Governance. This is a very new charity without many results yet. However, their website, working papers and trustees give them credibility and their plan for how to have an impact is sound. I would like to see them funded for 2-5 years, without needing to think about fundraising.