Predictions beyond a year or two are notoriously invalid because too many factors can render them wrong. But for the fun of it, I'll take a shot here.
I'll get the bad news out of the way first. My guess is that 100 years from now, we'll have suffered a near Armageddon. The dramatic miniaturization of weapons of mass destruction make it too likely that a solo actor will have, for example, opened a vial of mutated highly communicable, deadly smallpox virus in the lobby of the international terminal of a major airport, infecting hundreds of people who are headed all over the world. Before a cure could be invented (Remember it's mutated and so no vaccine would exist), much of the world's population could die. Of course, almost no one would be crazy enough to do that. But among the billions of people on the planet, it only takes one person, for example, one disgruntled, demented scientist.
Because of that and advances in clean-tech such as truly safe nuclear power, we'll worry far less about environmental degradation.
I'd imagine we'll be transporting ourselves in nuclear-powered flying cars that can take off vertically from whatever parking spot we're in.
We will have determined what gene clusters cause the major characteristics in humans: intelligence, impulse control, predisposition to cancer, heart disease, and diabetes. Prospective parents will, at their election, choose to ensure their children have good genes for such characteristics. Most parents will eagerly take advantage of this. Government will make that option available free to the poor as part of its Single Payer health plans. Life Expectancy will be 110, nearly all of it spent in good health. The right to assisted suicide will be ubiquitous and widely used among those in severe, likely irreversible pain.
Because nearly all people will have high intelligence, greater efforts will have been made to automate menial tasks. So robots will replace humans in everything from busboy to janitor, ditch digger to cab driver. (You'll enter a cab, enter your desired address, and be flown directly to your destination. Sensors will prevent crashes.)
Asia will become dominant, America just a large midlevel player, exceptional mainly for its diversity. There will have been minor civil-war-like skirmishes but America will have become the true salad bowl envisioned by today's diversity activists. Privately, people will still choose to socialize mainly with people from similar socioeconomic and ethnic backgrounds but, in the workplace, differences will be grudgingly accepted as "just the way things are."
The academic side of education will occur outside of a school. Each student will use his SmartPhone with a screen that folds out to 8 inches to take mini-courses taught online by dream-teams of the world's best instructors. These will be interactive and simulation-rich. Testing will all occur online, of course. Students will sign-in using iris-recognition technology. Small-footprint schools will exist but mainly for extracurricular and socialization activities.
Politically, the world will have continued its leftward move. National sovereignty will be giving way to one-world government, with much redistribution from wealthier regions to poor ones. I believe that because the Have-Nots have more babies than do the Haves and they vote for liberal/redistributive governments. Also, many of the Haves feel guilty about their wealth and the media and colleges exacerbate that with such theories as "white male privilege," which implies that sexism and racism significantly affect people's success.
How would I live in this new world? I'd probably choose to earn my living as a physician. I've always been in awe of the miracle of the human body and value life immensely. I'd consider it a privilege to help people extend the quality and quantity of theirs. My career counseling clients consider me a good listener, which is critical in a physician. I'd be additionally attracted to the medical profession 100 years from now because science will have advanced enough that so many currently difficult-to-treat conditions will have ready cures.
Avocationally, I'd, as I do now, look to champion causes for making the world better that are not widely supported. That way, I'd feel my individual efforts would make more of a difference than if I simply jumped on an already large bandwagon. For example, I'd guess that 100 years from now, a commonly supported cause would be calls for yet more efficiencies. Because of that, I'd probably be a counter voice: reminding us of the importance of kindness, of smelling the roses a bit, and of pets. Indeed, one thing I wouldn't change in my life, even if it were 100 years from now: I'd try to find a pet as sweet as my doggie Einstein.