I've become sort of familiar with the city over the last few years because it is now part of my coverage area and I'm out there six times a year or so. With that said, here are some weird things I've done in Vegas and you should try:
Pinball Hall of Fame -- Pinball is awesome, and this joint has thousands of pinball machines. It's really cool.
Tour of the Neon Boneyard -- All of the neon signs from Old Vegas and defunt hotels and whatnot in one place. It's really cool to see.
Classic car display at the Quad -- if you are into old cars, that's kinda sweet.
Minus 5 at Mandalay Bay is kinda weird (but sort of meh) -- They give you a parka and let you drink vodka in this room that is - 5 degrees. The bar is made of ice. It's not that impressive but it is weird. This is a chain, I think.
The Peppermill restaurant is kinda cool. Great food and it has this weird 1970s vibe with neon and pink plush.
At Todd English Pub at Aria they will give you free beer if you can drink it in less than 7 seconds. I think there is a limit of 5, but it's a great little challenge because you pay 9 bucks or so if you fail the challenge. The bartender waived the limit once and my buddy Pops took the place for 8 free beers.
Helicopter tour of strip looks pretty cool. I've never done it, but i know it can be done for a reasonable price.
People have already mentioned the indoor skydiving
That's a good start.