It's certainly physically possible to travel somewhat relativistic speeds (and slow down at the destination) with antimatter fueled Von Neumann probes. Humanity (as organic life) won't make the trip to more distant galaxies, but its possible our technological descendants will.
If we assume the 4 million LY to the most distant Local Group galaxy is a surmountable distance, its only one more jump in magnitude to the next clusters like the M81 group or M83 group (11 million LY) or the rest of the Virgo supercluster 24-40 million LY.
It's one of those "deep time" limitations that i don't really care about.
In a trillion trillion years all atoms that existed will have been ripped apart and decay into useless infra red radiation, so be depressed!
On a more relevant note; unless you conquor a good chunk of the world and/or murder millions of people chances are your existence will be forgotten in less than 100 years
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