I’d stay in my current house, but I’d probably remodel it a lot. Like, I’d turn my 2-car garage into a commercial kitchen and build another 2-car garage somewhere else.
I would, however, travel a whole fookin’ lot.
And, given that I’m rich, I’d hire a personal assistant who would have to come and take care of my dogs & the house at the drop of a hat whenever I wanted to travel so it’d be totally easy.
OK, I’ve talked myself into it. Where’s my money?
I wouldn’t travel too far - I’d like a place on the Chesapeake Bay, maybe on the eastern shore so I could enjoy sunsets over the water. It’d have to have deep enough water that we could moor our boat right there - that could be tricky, since the Bay tends to be pretty shallow near shore and we’d need 7’ at mean low water. I’d like the property to be big enough that there’d be no direct line of sight from my house to my neighbors. It wouldn’t need to be a huge place - no more than 2000 sq ft with a two-car attached garage and an outbuilding for my studio and my husband’s woodshop. And if it came with a landscaper, it’d be perfect! 
I’ve thought about this A LOT. I currently live in the middle of the pacific ocean on a small rock filled with idiots. Some people THINK it’s paradise, because they weren’t forced to live here. It’s practically a drug death trap, nothing for the younger generation to do, and pretty much holds onto old traditional mind sets. Hawaii can be beautiful, but really it’s for visiting and for old people to retire… 
Right now, I really really want to go to Sicily! I think the culture would be rich, the weather amazing, and the food and drink spectacular. Of course the people, beautiful. I was never one for tropical weather, and I’m not sure if Sicily has seasons, if not, no different than Hawaii.
My second choice would be Scotland just because!!! Oh the Scottish accent… -sigh-
There are many many more places, last time I made a list, there were about thirty… So I’ll just make it three or well a tie between New Zealand and Canada, Montreal to be exact.
If I got loads of money, I wouldn’t blow it on big stupid useless things. It’s smart to think small and then still have money to live over with. I believe it’s just a condo there for visits anyway.
I don’t think I’d move, but I’d spend a lot more time traveling. Why bother with buying a new house somewhere, when you can stay in the 5 Star Hotel of your choice in every city in the world?
My husband would insist on Florida or Georgia (family) but I have family in Seattle. I might be able to talk him into wintering down south and spending summers around Seattle – Port Angeles or Sequim are appealing.
I’d stay here in LA, but would probably move to west Hollywood or the Hollywood hills.
The same city I’m in now, but in much more luxurious accomodations.
I can’t see myself buying a house anywhere else. Vacations are fine, but living in multiple places would be disruptive to my kid.
First I’d make sure my son and grandkids are set up for the future, and give some bucks to my siblings and their children. Then I’d go back home to Ventura County and get a place at the beach. I’d get a second home in Antigua & Barbuda, also on the beach. Six months here; six months there. Oh, and lots of other traveling too.
I like a lot of things about Oregon, including the weather, the attitude, and the conditional legality of certain otherwise-illegal substances. I don’t think I’d spend all my time there, though. I’d be there a lot, and I’d call it “home,” but I’d also buy a few places elsewhere–one in New York City, one in the Virgin Islands, and maybe one in my Indiana hometown–and spend different times of the year in them according to the weather/my eccentricities.
I’d stay in the same area but I’d buy a nice four bedroom house and rent out two rooms to my two current roommates for cheap.
Still here in Napier, New Zealand, for all the reasons I’m here now. But I’d buy a newish, 3bdr, low maintenance place on either a easy access hill site or rear on-the-flat.
That should leave enough for keeping a small pied-a-terre apartment in Auckland that could be a short term rental source of income if I’m not using it.
Northern New Jersey, near my birth family. Tho I’ll be doing it anyway lottery or no.
Homes in NYC, Sarasota, Los Angeles and Cancun, Mexico.
I’d probably stay where I am now (somewhere in the south). I just bought a house in November; I’m happy with the location; I’d probably do some major remodeling. I have a lot of land so I could build some pretty kickass stuff - workshop, etc.
I’d probably buy a (modest) house back home in Kentucky to stay in when we go visit my Granny, which would be MUCH more often than now. I have a cousin that could really use a free place to live and she’s one of these compulsively clean types so I’d let her stay there that way the place doesn’t go to pot when we’re not around.
Pending discussion with my wife, of course, I’d be inclined to stay in the LA area. It’d be easy to live somewhere that being wealthy wouldn’t make me stand out, and I’m paranoid enough to be really concerned about people knowing I had that kind of money. So even though I don’t care at all about being around celebrities, I think what Antinor01 suggested with the Hollywood Hills would probably suit me under the circumstances.
However, I’d spend half of the year traveling to wherever the Dodgers and Indians were playing and enjoy getting to visit all of the major league baseball stadiums, so I’d “live” in a lot of nice hotels, I’d guess.
A house in the mountains, one at the beach and one in the city.
Aspen, Rehobeth, and Philly.
I think I’d like Costa Rica.
Ithaca for my main home. If I work long enough I’ll be able to retire there anyway, but rather than work an insane amount of time to get a really good home there, in reality I’d prefer to save a few years of working and just buy an okay home. But with the lottery I’d be able to get a pretty big home in a prime location within [del]walking[/del] easy strolling distance of the gorges and downtown (everything’s within walking distance of gorges in Ithaca!)
But I’d also do some travelling in the British Isles first. I might get a second home there if there’s a place I like well enough. Don’t know if I’d commit to a home as I haven’t been there yet, I might prefer to just travel a lot.
Other places in America I might visit a lot but wouldn’t want to live there for more than a couple weeks. There are a few other places in Upstate NY that are almost as desirable as Ithaca but they either don’t have the population to support lots of potential friends, or they’re not in as beautiful location. But I’d still prefer them (Oneonta, for instance,) to most other places in America for a permanent home.
I’ve thought about this. Definitely a condo in Boston, because Boston is great; a place in Hawaii, because sometimes I want it to be warm; a secluded retreat/fortress in Sweden, because sometimes I don’t like being in America (usually this happens in election years) and why wouldn’t I do that?