The sad reality is that we can't do much about the laws of physics. Even 100 years from now it will take the exact same amount of energy to lift up anything from the Earth gravity and get it anywhere. Unless somebody invents a de facto new law of physics what we have no idea about today, that is an unavoidable starting point. It took an over 100 meter tall Saturn V rocket to lift up everything what was needed to land on the Moon and finally bring back a tiny capsule with 3 astronauts.
Well, one doesn't have to change laws of physics. We just have to develope new propulsion technologies. I give you a perfect historic example: 100 years ago, in 1910, all airplanes were propelled by piston engines. Back then, beside only a very few aviation pioneers and visionaries, almost nobody would have ever expected that an airplane, consisting of metal with a mass of more than 200 tons empty and more than 500 tons at maximum, carrying 800 passengers, would be able to lift off the ground, heck, even fly with a speed slightly below the speed of sound with a range of more than 9,000 miles. Not to mention Concorde: 180 tons including 100 passengers @ Mach 2.0 (without reheat, which was just used for acceleration from Mach 0.9 to 1.7).
And now imagine that all started with the invention of the wheel, the steam engine and electricity. Think about the telegraph and a modern mulimedia cell phone. And so on...
Our scientific and engineering history shows how difficult it is to predict future innovations. And it especially shows human capabilities. Progress is not over at all. Quite the opposite. Progress is as fast as never before. We're just used to it, which creates the wrong "feeling" that we're approaching a hold. Just compare the one man Mercury capsule to the Space Shuttle and the ISS. And it's still just the beginning. There is more to come.
Mars mission with people with the existing technology. Very, very unlikely.
The unlikeliness is not really related to the current technology. Our technology would already allow us to perfectly fly to and land on Mars. The only issue, beside that such a program would cost several 100 billion dollars, is time, i.e. the long term effects of weightlessness to the human body.
Going beyond the Mars....well....where exactly? And how exactly? We have the gas giants and their moons. Anyone who is familiar with the involved distances and traveling times should know that again, with the current technology they are simply not available for us (with humans). Even more sad, that even if they would be, the probability of finding anything radically worthwhile or interesting is very small. Beyond the solar system? The first and nearest stop would be the Alpha Centauri, "only" 4.6 light years away. And we have no idea whether it even have planets around it.
I agree that, from a present-day perspective, manned missions beyond our solar system seem to be utopian. But remember that when Columbus was discovering the northern American continent, nobody would have ever thought that it could be possible to "fly" over the Atlantic Ocean, in things of metal called airplanes, with a speed slightly below the speed of sound. Less than ever to travel into space and live there for ~6 month while the whole world can watch it live via a thing called "internet"
It's all really about present-day perspectives only. The world in the year 2110 for sure will look significantly different in compariosn to the present day.