I’d probably buy a place in Oregon because I’ve always wanted to move back there, but I really just need one house. One awesome home base in the trees and then the best hotels for my travels.
Top floor of the Trump Tower in Chicago is still for sale. Over 14,000 square feet. That’ll do.
I’m too attached to my pets and to family, and to the feline rescue I work for (which would get an enormous donation plus trust) to leave.
Upcountry Maui.
I would buy a house in the Manoa Valley of Honolulu, Hawaii and split my time between Bangkok and there.
I would buy my dad a house and a new car and help the needy people in 3rd world countries, travel a bit and help out some of my family members.
I would personally find a nice chunk of land out in the country to build my dream house–a sprawling Southern Plantation style house with a wraparound porch absolutely covered in rocking chairs and droopy-faced hounds. 
I’d stay right here at home. But I’d build a house with all the features I want. I’d fix the house up that I live in now(upstairs) and either give it to charity, or to my tenant downstairs.
I’d give a lot of the money away, to church or other favored local causes. Can you hire a lawyer to act as an intermediary, so the money could be given anonymously?
My major fantasy is to give every church that the Westboro Phelps clan pickets $1000, every time I see them outside before services. This would go for the synagogue and the Islamic Center as well, but I don’t know if they’ve picketed there. I’ve only seen them outside of Christian establishments.
I would stay in this area–I like it here. I’d probably have a house designed and built to my specifications, someplace like Los Gatos or Los Altos Hills or Atherton. Probably Los Gatos–it’s one of my favorite towns in the area.
I’d make my base a home in the Colorado Front Range, keep a condo here in Milwaukee for return visits, and then have 1 more condo in either Portland or Seattle.
Lots of traveling, as others have said, and multiple residences, possibly starting in New Zealand. More probably, NZ would be #2 on my list of places to live (outside of the US), behind this place.
I’d stay in Sydney but I’d buy an apartment (a really nice one) overloooking the harbour. Milson’s Point, maybe. Or Manly.
I would live in my current home, because it’s perfect. But I would travel a lot more, and maybe buy a condo in several places I really liked.
Chapel Hill, NC would be nice, with the mountains at one end of the state and the ocean at the other. Not only is it a university town, it has a lot of “writers-in-residence.” Imagine the soirees.
I like where I live. So I’d stay here in Melbourne AU somewhere, but in a custom built home of my own design to accommodate my peculiarities.
I’d also try to have it encompass enough that I’d be able to minimise the need to leave it for any domestic reason, and yet always feel comfortable, never trapped by its confines.
I would buy a home in Hawaii to spend the non traveling winters in and build a home outside Toronto for the summers. I wouldn’t have to worry about seeing friends and family, in fact the requirement for the Hawaii house would be a guest house as well in order to have any time alone
The only downside to this plan is the dogs. Hawaii has a 6 month quarantine requirement which means I need to pick a house for them to stay in. That’s probably only a short term issue however 
Stay right here in Las Vegas.
With current housing market, you can get huge homes for 1/2 price in great locations.
Also, Las Vegas has a great airport that could get me to any location in the world for vacations, often non-stop.
With that much money, why would I buy a vacation house to upkeep when I could easily stay in a rented villa or penthouse of luxury hotel wherever my whim took me?
Sure, Hawaii is beautiful but after two or three winters, I might like to try Bangkok or St. Thomas or Fiji or a Greek island instead.
Yeah, that’s my thinking, too. I could also see renting a villa for a few months at a time in various places. I don’t want to hassle with ownership much. I might buy some land somewhere in the wilderness and preserve it through a trust or something.
I have a great piece of land picked out that I’d like to start a vineyard on and open a winery. I’d also build a nice - not extravagant, but nice - house overlooking said vineyard. It’d have to have a pool, nice entertaining areas, etc.
I also fell in love with St Thomas, so would have to have a condo or small villa or something on the beach or a nice huge cliff on St Thomas.
Aside from that, I can see a huge portion of my lottery money going to a couple specific non-profits.
I’d probably keep my home base in my current town. While it may not be perfect I like this area of the Jersey Shore, especially in the summer. I’d probably trade up into a larger house with a bigger yard though. Nothing monumental, just something with a little extra space for things like a pool table, a library or study, and maybe a home gym.
I think for the first 5 or more years I’d be traveling extensively around the world and returning home for a couple of weeks or months at a time. Eventually after doing a bit of exploring I might decide to buy a couple of apartments, condos, or small homes in some spots that I’ve discovered. I can’t imagine I’d have more than 2 or 3 “second” homes though, if that.