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Galaxy map.
What I would do is just go to the next nearest destination to you on your list that you are closer to than you were at your previous destination(You'll need to keep a little spreadsheet of these distances and update it at each destination). That is going to be darn close to the optimal route.
That is fine to get to each destination beyond 1000ly, but from how I undestand OP has 20 target systems he wants to visit, not only one.
OP is basically asking for a program that makes his passenger/delivery/data missions easy, it's two separate issues.