There are many writers from the past and present but who comes closest to projecting where Humanity might be in 50, 100 years?
(Hope I'm framing this right.)

Not sure there's any such thing.  People who write SF make fun stories first, accurate predictions second(or tenth, or whatever.)

There's really no right answer.  Read SF from 40-70 years ago, some AE Van Vogt, or Asimov, or early Clarke and Niven.

Most authors get a few things right (my favorite example is the 1946 story 'A Logic Named Joe' by Murray Leinster, which arguably predicted the internet, though the specifics were not all on target), but for the most part it boils down to 'cutting edge or near-future tech will have way more of an impact on life than in reality, real life developments are fully missed'.

Think of some classics, like Black Destroyer, or Neuromancer.  Good stories, but at this point it seems pretty clear that nuclear fission will not take us to the stars, nor will AI coexist with payphones.  In fact, William Gibson quit writing fiction because he couldn't think of shit that wasn't going to be superseded within his lifetime.

It's hard-to-impossible to fully predict the future.  It doesn't look like 2001: A Space Odyssey, or Blade Runner, or Back to the Future Part II, or Robocop.  All of them got little pieces, but none really got it right.

Weirdly enough, I'd have said Snow Crash was fantasy with SF trappings twenty years ago, but some aspects of it seem to have become more prescient over the years - IE the erosion of governmental power and the rise of private/corporate power.  Hell, even the power of memes, which seemed a little silly at the time, but helped a president win his seat in the present.

So where does that leave 2067-2117?  Who knows?  If you read enough SF that's set in that bracket of time, you'll know some of what's coming - as well as a bunch of shit that'll never happen.  And as far as which of it is true?  Well, that's as opinion based as the works of the authors, and with probably less fact and research to back it.  

I'd guess Alastair Reynolds probably has some of it right - Pushing Ice is set in 2057, with the cast of characters in a fusion-powered spacecraft for asteroid mining.  Minus the "Janus is an ice-covered alien probe", I'd say that's reasonably accurate (though I'd push it back a decade).  Kim Stanley Robinson had a very well thought out journey for the first Martian colonists...though he put the date at 2026 (and nowadays I'd push that back by 20-25 years).  For my own amalgamation of ideas, I'd say that in 50-100 years from now humanity will have: colonies on Luna, Mars and Ceres, with workplaces in the Kuiper belt and on at least one Jovian moon.  Life extension that, at best, will allow for a 150 year average lifespan - for those who can afford it.  For those who can't, basic healthcare will be provided, along with a a basic living allowance and a subsidized living space.  Various diseases will be cured, some others will have treatments that don't cure but extend the life of those diagnosed.  There will also be new diseases that arise, and medical science will be hard at work dealing with the drug-resistant forms of bugs that are otherwise stamped out.  Corporations will wield as much power as some governments (which isn't anything new, really, just look at companies like the Dutch East India Company, or United Fruit - money gets shit done no matter who is holding it.)  

If the trends over the past several dozen decades are to hold, the life of the average person will continue to improve overall, and yet the lot of the creme de la creme will improve exponentially more.  So a poor person in 2095 will be nearly guaranteed to have a roof over their head, data access, subsidized food and medicine, and good public transportation.  But robots/AI will take over most jobs, leaving it tough to find real work.  And the handful of people at the top will pay insane taxes to support everyone else, but will still have the kind of money it takes to buy private islands/asteroids/spaceships and maintain complete separation from the rank-and-file.

But given where SF authors of 50-100 years ago thought we'd be today, there's maybe one thing that I just mentioned that's actually going to come true, and even then it'll be in some way that neither I nor the person who came up with it could have ever have dreamed up.

Mike Judge

Culturally, I would have to say Neal Stephenson and Peter Hamilton but in different ways.

For Stephenson it is how near future hard tech will impact humans as a society.

For Hamilton it is how far future longevity is going to affect human culture.

Niven and Cooper really hit far future longevity (via suspension) and class warfare amongst two varied types of high tech societies in Building Harlequin's Moon.

Marko Kloos - Terms of Enlistment.

I think the portrayal of the planet is going to be fairly accurate down the road, he may even have the timeline pretty spot on. If humanity exists long enough.