For the past few months I've been using Barba Ring in LP 355-65 as my "home base" because it's a Li-Yong Rui system with almost everything available in outfitting. However, I acquired an Imperial Clipper today and decided I wanted a new place to hang my flight helmet with a large pad, a shipyard, and no mailslot. (It's not that I can't ring the slot, it's just that I don't want to if I don't have to.) Since we don't have fleet carriers yet, I started looking for a megaship I could call home, since that would fit all my criteria, except I discovered that almost all of them do not have a shipyard.
Enter Tiliala’s Lament in the Akandinigua system. It has full rearm/repair/refuel, outfitting with most modules available, a shipyard, and most importantly, large pads without a mailslot. It is also unique among this class of megaships in that it does not move, i.e. it stays in orbit around planet 5 permanently instead of jumping on a schedule.
So there ya go. If you're looking for a place to park your fleet for the next couple months, you might consider Tiliala’s Lament.