I find time dilation confusing so I'm not sure if it is a relevant factor.
Lets say you have a spaceship. There's no such thing as faster than light travel, but you do have inertial dampener technology that allows you to accelerate at very high G's without obliterating yourself.
You want to get to a nearby star system as soon as possible. When I say "soon" I mean early on the timeline of the destination star system, not necessarily as quick as possible according to your own perspective of the voyage duration. In other words, you want to intervene in the events of the destination before they progress to far into the future.
Is there a maximum rate of acceleration or top speed you could reach before time dilatation causes you to actually arrive later than you would have at a lower speed?
What about if you want to go there and then get back before your friends at home get any older?