With a constant 1g acceleration up until near the speed of light you can cross the observable universe in a human lifetime.
To the other side of the galaxy it would be 12 years
https://en.wikipedia.org/wiki/Space_travel_using_constant_ac...
To the other side of the galaxy it would be 12 years
https://en.wikipedia.org/wiki/Space_travel_using_constant_ac...
Going to Mars using antimatter with the same 1g acceleration the entire time (reversing half way) will take a few weeks and require a small fraction of a gram of antimatter.
Ignoring the significant engineering problems like heat disappation, storage if it's not used instantly, you could get two years worth of thrust from antimatter measured in grams and cross the galaxy in just over a decade, in Earth time the trip would be >100,000 years.