Sure, with the comfortable acceleration of g during the first half of the journey and decelerating during the rest of it, I could arrive to, say, Andromeda galaxy in a few dozen years. The biggest question, though, for me is: OK, I’m here, now what? (Having a vivid imagination, as a child I once imagined myself standing on the Moon’s surface, looking at the distant Earth shining just above the horizon and the eerie landscape below. The first and the only thought I had at that moment was: “What the hell am I doing here?”)
The year is 1492. You're imagining standing on the shore of a vast continent, unexplored by your people. The only feeling/thought you have at that imagined moment is “What the hell am I doing here?”
That is perfectly reasonable! But I hope you can appreciate that the imagined feeling/thought is not shared by everyone.
That's not very comparable, because you could easily live a very fulfilling life in a new continent (well, except Australia, I guess?), but being on the surface of the moon would be a constant struggle for survival.
Explorers do not become explorers from a wish for "easily living a very fulfilling life". There was nothing guaranteed about the quality of life offered by the great women and men who traveled the seas in ages past, and indeed many of them perished.
No, colonizing a new continent was not "easy". It, too, was a constant struggle for survival. New pests, new climate, new soil, new flora and fauna, communication (or battle) with natives, etc.
You could live a very fulfilling life next to Sydney Harbor, or Melbourne's Port Phillip Bay, or... well, anywhere that people have lived in Australia for the past 50,000+ years.
This is also a very eurocentric point of view that ignores that people were already living in the Americas. What happened in 1492 was not grand explorers finding undiscovered country in the star trek sense. It was conquerers finding a new land they were ignorant of rich with resources they could take by force via superior military power.
