If I were super rich, I would do quite a bit of investing so that I could continue to be super wealthy for the rest of my life and make it so my kids are set too. But once that is out of the way I would continue doing all the things I've ever dreamed about.
I would like to open a university that focuses on math, engineering, technology and all of the sciences, as well as useful trades like auto repair or HVAC systems. I would not have any of these free floating, do whatever sort of classes and majors. I also would not support the arts at my school as I feel that is something you teach yourself about, although I wouldn't turn away anyone from wanting to hold a performance or show at the school, just no classes. I would keep the cost reasonable and run it very tightly so that more students could afford to go to school.
I would also fund many archaeology projects, I feel it is important to know about our past and I feel like we don't do enough to uncover and preserve it. I also would also keep paleoarchaeologist well funded so that they could afford to find out the human ancestral lineage.
I would donate money to charities that actually make a difference in peoples lives instead of paying the brass within the organization obscene amounts of money. I would also create my own cancer foundation that would not only fund research, but would also knock Susan G. Komen's "charity" off the map. I would also fund research of Alzheimer's as well since my grandpa suffer from it, I also would build a new facility for the nursing home he's currently in since they have provided excellent care. I'd open up my charity fund so that anyone that feels they have a noble cause worth funding could make a request for money. Solving a lot of the problems in the US would be pretty noble, and I doubt I would focus much on other countries.
I would invest in small businesses that I think could actually do something and grow, it would help jump start the economy and allow people to pursue the American Dream. I would also have directors setup to help these people too so they aren't just given a bunch of money and told make something with it. While doing this I would really try to revitalize Detroit by helping to clean up neighborhoods, lower crime and build successful businesses.
Then I'd buy my toys, a Gulfstream G650, Infinitas yacht by Schöpfer Yachts (check out pictures), a Sikorsky S-434 helicopter for said yacht, a Bell 525 Relentless with a custom cabin for short jaunts and a Rolls Royce Phantom so I can be driven places. I'd also buy a Piper Seneca V and get my pilot's license. I wouldn't want many cars, when you're ultra rich there are better ways to get around than worry about driving yourself. I'd still have 1 or 2 at my homes though, maybe something like a Ferrari California or Lambo Gallardo Spyder for the warmer areas and something like a Land Rover for the snowy areas, oh an Ford Raptor while I'm at it because why not.
I'd have a house in Alaska, north of Anchorage, on a massive piece of land so I could get away and not be disturbed. This would be my summer residence and I would head to a winter home in the US Virgin Islands. I'd also have a vacation home on the island of Ibiza, Fiji, northwest corner of Michigan, and one somewhere in the Swiss Alps with ski in-ski out access to some resort.
I'd have a house built for my parents, probably somewhere in the US Virgin Islands as well. I'd also have vacation home built in Minnesota on a lake so they could enjoy that too. After that anything they wanted I'd make sure they had. Probably do the same for my close friends too.
Past that I would just hand out money to people on the street. See a homeless guy in a wheelchair, just walk by and drop a $100 bill in his change cup, or overhear someone on the phone talking about how they are about to lose their house because they just lost their job and hand them a wad of cash. I'd also probably buy a whole bunch of toys and go around to children's hospitals and do what I could to make the kids feel better, kind of like that Batman guy and his Lamborghini. Fulfilling kid's last wishes is another thing I'd do, they want to go to Disney? Book their entire family a resort and give them spending money to have a blast and create memories. I know people go on and on about how money won't buy happiness but I'd be pretty damn happy if I could help other people like that and restore faith in humanity.