We kind of have – the Voyager 2 probe has officially left the furthest reaches of our solar system. It’s only taken it 30 years to get there 😐
So with the same technology (and judicious use of gravity assists) it would be possible to get there in 30 years. But actually there’s nothing out there. Like, NOTHING. So it wouldn’t be very interesting. The more exciting thing would be to get to /another/ solar system, which would take thousands of years.
It’d take a little while for us to develop the technology that could take people outside the solar system. We need to completely understand how the plants we’ll use to make oxygen work, so that they won’t all die for apparently no reason and leave the astronauts to suffer. We’d also need to work out a way of making food, and health products in space, because you’d never be able to take enough with you…
Even if we started working on it now (and we sort of are, the oxygen and health thing is what I’m doing for my next job), it would take tens of years to get it up and running. And then, like Adam said, it would take 30 years to even get there, and even then it’d be a one way trip.