There's a type of rollercoaster ride called a drop tower - it's basically a vertical pole or strutwork tower with a track running down its sides, and the cars are simply dropped from it and have a few seconds of total freefall. Some versions slow the cars to a stop as they approach the bottom, while others curve to the side and impose a few g's on the curve-down. Examples:
(Credit: Loozrboy at http://commons.wikimedia.org/wiki/Fi...ember_2009.jpg
(Credit: Ben Schumin, at http://commons.wikimedia.org/wiki/Fi...ng_of_drop.jpg
(Credit: Ben Schmin, at http://commons.wikimedia.org/wiki/Fi...wer_ascent.jpg
(Credit: Dreamworld_Tower_from_Nick_Central.jpg: Mark & Danielle マルチン f, at http://commons.wikimedia.org/wiki/Fi...Dreamworld.jpg
(Credit: Hywel Williams, at http://commons.wikimedia.org/wiki/Fi...k_-_145471.jpg
(Credit: David R. Tribble, at http://commons.wikimedia.org/wiki/Fi...Tower-5943.jpg
Anyway, once you get over the sheer terror of these rides, they're actually quite addictive - zero g is something your body learns to crave with a kind of spiritual yearning. Unfortunately, I don't have and will never have the balls to jump out of a plane, so skydiving is out, and parabolic-dive plane rides that offer about a dozen 20-second bits of zero g at a time cost roughly $5,000. In other words, my options for exploring this "hypogravitic" fascination are limited.
This in mind, I couldn't help noticing the fact that these drop tower rides never rise any higher than a few hundred feet, while skyscrapers are now routinely over 1,000 ft tall, and the tallest of tall structures (Tokyo Sky Tree would definitely apply for this purpose) exceed 2,000 ft. Now, there's no physical reason a simple, guy-wired truss tower with a drop ride couldn't be built to these extreme heights, but I appreciate that it would be impossible to keep in operation if that were its only function. A loud, hot, high-velocity coaster ride doesn't seem compatible with an EM antenna, so that's probably not an option. So then I thought, well, instead of using a drop tower as something else, why not use something else as a drop tower?
And that brought up a memory of something I used to do as a kid, that may or may not have been normal: Whenever an elevator would start down, I would jump up as high as I could, and for just a split second the combination of my jump and the elevator's downward acceleration would leave me falling for a lot longer than I could have safely managed in an inertial reference frame. That, in turn, left me wondering why - given sufficient height - the damn things couldn't just be allowed to fall freely and then slow down gently toward the lobby. I know the answer of course: Most people would avoid such an elevator like the plague, and it would cost far more than a regular one to build, maintain, and insure, nevermind the regulatory headaches.
But still...none of that changes the fact that it would be awesome. And being in an enclosed space means you can turn it into a vacuum tube and avoid hitting terminal velocity, so there would be no inherent maximum weightless time apart from the height and the tolerances of the system. The interior surfaces might have to be impermeable to clean up the occasional vomit, and perhaps have seats with various restraint features - still worth it, IMHO.
And like a parabolic plane ride, such an elevator could allow itself to fall at accelerations beneath freefall, permitting moon gravity or Mars gravity. Perhaps there could be separate elevators for each? If I feel like taking a 5-second detour to the Moon on my way to lunch, I could take the requisite elevator. People have been complaining for some time that it takes too long to travel in very tall structures...well, there you go. Drop express elevators. People taking them down don't have to wait while it descends, and people taking them back up don't have wait for their ride to arrive.
Hell, they don't even have to necessarily go all the way to the bottom - just have separate tracks curve down horizontally to any given floor, if there's a lot of inter-floor activity. It might be quicker to get to 60th floor by taking the express to the 75th and then dropping 15 floors. Anyone likely to use such an amenity would be more than willing to pay a premium for the privilege - I know I would. It would be invigorating, but not nearly as potentially nauseating as a rollercoaster - after all, you only take an elevator down a few times per day, and dramamine is cheap.
Regulatory issues mean you couldn't call it an elevator because of g restrictions, but whatever. Call it something else, only allow entry via a payment card or something that involves signing informed consent releases, provide them with a 5-minute safety video to view or not at their discretion, put up warning signs inside the elevator, and make sure everything inside is soft, cushioned, and curved.