I am looking for a place to sell one of my ships and want to know the fastest way to get there to get a decent price.
Since there are many different starts in X3:AP and most starts put you in a random sector within a part of a galaxy, its not possible to say what the 'closest place' is. But here are some guidelines that may help:
There are a few factors that goes into selling a ship:
To find the nearest shipyard at your starting location, just open up communications with random ships or stations and ask them which way to the nearest shipyard. Unless you have bad rep with that race, they'll usually direct you to them.
Finally, you can look up the location of a shipyard using the Universe Map. This is a X3:TC version but the X3:AP shipyards are in the same sectors as not much as changed between the games.