For me, I'd plow huge amounts into education, as I believe this to be the most viable solution to so many of the world's problems. To raise the quality and range, ensure everyone falls in love with learning and make it the respectable profession it again deserves to be. Then there might be a little cash left over to revamp public transport and market it as the enjoyable, affordable and sociable way to travel it should be.
Town centres should be places with dignity, and a sense of public importance, where it's nice just to sit around, have a drink, read the paper, and buy what you want to buy.
What would you do with unlimited funds?