Right now, it would be very difficult to get to other planets. We've got maybe three within this solar system that are habitable with extensive terraforming (I'm thinking of Mars, Venus, and Europa - okay, that's a moon, bite me) and, while we might be able to get to Alpha Centauri with a truly spectacular effort, it's doubtful there's a large number there. So imagine we invent a star drive capable of traveling at the speed of light - now we've got half a dozen barely-habitable planets, if we're willing to spend four years to get there.
Most science fiction star drives tend to be surprisingly slow. Larry Niven's hyperdrive traveled at the blazing speed of 110 times lightspeed, allowing you to reach other stars in mere weeks. Star Trek is spectacularly inconsistent, but seems to vary between 2500 times light speed and around 5 million times. Star Wars approaches ten million times lightspeed, although that's a reference point based mostly in offhand comments and speculation.
Ten million times lightspeed is very fast. But by the time of Star Wars, many planets are colonized and many many alien races discovered. The galaxy is "full" - it's demonstrated repeatedly times that warping around randomly will rapidly land you next to someone's home planet. Humanity's expanded quite a lot since they invented their hyperdrive, and - one presumes - they started with a much slower engine.
Even at ten million times lightspeed, a velocity that lets you reach the other end of the galaxy in four days, Andromeda's over half a year away. What would happen if we invented a warpdrive that made that practical *today*?
Let's say we invent a device tomorrow that allows you to move at eight trillion times light speed. I didn't pull that number entirely out of a hat. That's how fast you would need to be to travel the estimated diameter of the universe in a week.
This would let you reach Alpha Centauri in approximately 17 microseconds. If you wanted to circle the galaxy, you'd spend slightly more than a second doing so. In five minutes you could visit Andromeda and come back . . . thirteen times.
Within our own galaxy there are enough stars for each man, woman, and child on the planet to own ten of them, and still have breathing room for another decade or two. Within our universe there are enough galaxies for each man, woman, and child on the planet to own ten of *them*. With this warpdrive a million explorers could spend their entire lifetimes discovering new planets, and still return home in time for lunch each day.
It would be utterly impossible to find someone you were looking for without coordinates. Even if they built a neon sign a light year wide pointing at their home. If you wanted to take a sabbatical from humanity, just point your ship in a random direction and fly for a day, then pick a galaxy. It's yours. Enjoy. Come back when you feel ready.
Of course, even if it wasn't yours, you'd never know. Assume you can build a sensor capable of scanning a globe ten light years wide. (Realize that this would cover several stars.) Assume you want five minutes warning for someone entering your galaxy. Back of the envelope calculations: you'd need a few quadrillion sensors to enclose your galaxy, and the incoming ship would show in your detection grid for about 40 microseconds. Your sphere would be approximately 152 million light years wide, and would likely enclose many galaxies besides yours. If your worst enemy was in the galaxy next door to you, you wouldn't know until he left the area or came visiting.
(You might be interested to know that if each sensor weighed one kilogram, you'd only need to convert about a billionth of the Earth into sensors.)
And if there's an alien race in your galaxy, you'll never find them. Some day your monitoring systems would beep at you, and you'd blink in surprise at a craft *leaving* your galaxy on its maiden voyage. And that's only if we have such sensors - without them we'd be effectively blind. One gets the mental image of a thousand different species, each one with billions of starships capable of bounding across the universe in mere days, none ever finding each other. It would be the equivalent of walking around Nevada at midnight with a pen light trying to find a specific pebble.
Nobody ever does this in scifi. I'm guessing because the numbers are just plain too large. They're hard to imagine. And yet I suspect there are stories to be told here.