There are a variety of bases ran by different factions in Freelancer such as Rochester, Planet Manhatten and even Buffalo Base.
With this little guide written by Dudeofthed will explain where all the base locations are. The names are given in sectors e.g A1, which means if you look on your Nav Map and zoom into A1 there is a base there given to you by this guide.
Please note that this site will be updated shortly after Dudeofthed will get the list from his Nav Map. He has discovered all bases with all the factions.