I would buy myself one of those 35,000 piece jigsaw puzzles and have a room dedicated solely to putting that thing together. It would have to be a “clean room” sort of room so I could be sure that no pieces end up missing.
My first answer was “Beer!”, then I realized I already have that (my man-cave).
So, my answer is a hidden Cannabis Growroom. My old house had one, but I sold the house to move in with my gf. I really miss it. It was a wonderful hobby. There would be separate arears for mother plants, vegetative growth, and flowering. Airflow would be forced through carbon filters.
Winning a billion dollars? I’d have an entire room dedicated to Getting Elected President of the World just because I could.
Forget about one room, with a billion dollars, my entire house is getting redesigned for the Star Trek universe.
Adam West.
Not a room full of Adam West memorabilia. A room to keep the actual Adam West. He’s nifty.
A library, but not the Beauty and the Beast type. I’d want one that looked just like the children’s room of my public library growing up. Wall to wall orange carpeting. Grey metal shelves, not just lining the walls, but lined up in the middle of the room, one after the other. And an old-fashioned, wooden card catalog.
Oh, I have such memories…
Plants. I want a large greenhouse conservatory with a Koi pond and free flying rescue birds and maybe some small lizards and frogs, too. I would add a couple of comfy chairs and a hammock so I could hang out in there and read and nap.
Yeah, I’ll be on the phone to these people pronto.
Any dough left over after shipping, construction, ancillary equipment, permits etc. will be used to hire people to water and move the heavy tubs.
Whatever it would be, it’d be accessible from a secret passage.
Gaming. Full size pool table, large board game table with customized DM station, multiple pinball machines and arcade games, multiple huge TVs with all major gaming systems w/multiple controllers, multiple PCs set up for games of all sorts…including WoW. Book shelves for storing board games, and rulebooks/miniatures. Easy chairs/couches for watching sports or games in progress, bar with soda, snacks, and large quantities of products lawful in Colorado and certain other states…
Cars, Cars, Cars.
My daily driver already has its own detached garage/man room/well appointed shop.
If I had a lot, lot more money I would have a Jay Leno style warehouse full of,
Cars.
This is room #2 for me.
Just a giant game room filled with every game I could ever want to play.
This sure sounds like The Salamander Room, by Anne Mazer:
You know what, on second thought I’d rather have a Scrooge McDuck style money vault room so I could swim around in all the cash.
The Gear Room, to replace my current Gear Closet.
All the skis, bikes, kayaks, camping gear, tools, and benches to work on them all.
A recording studio.
A room devoted to nothing but 70s culture. It would be so authentic, it’d be like stepping back in time.
If I won the lottery, I’m now a venture capitalist (I imagine something like the people on the show Shark Tank). My office would be a perfect replica of the Oval Office (complete with trap door under the desk*).
- I don’t know if the President really has access to a protective bunker under his desk, but I’ve heard the rumor.
Surely you want the trap door in front of the desk? 
Give me a chair that descends Thunderbirds style to my underground lair / garage / whatever.
Music Room with a vintage steinway upright piano and a extensive vintage guitar collection.
I’d include a mixing console board and other equipment for recording.
klipsch heresy speakers to monitor the sound.