I've run a fair bit of Classic Traveller in the last few years.
In 20+ sessions I can think of six maps that were used:
* When the PCs assaulted a military installation I drew a map (building it out of the roll for encounter distance); on a second occasion, when some PCs were prisoners in an installation, I sketched a map (maybe using the same technique? I can't remember now);
* We've had two ship plans: the St Christopher (from an old White Dwarf) and the Annic Nova (from Double Adventure 1);
* The alien installation in the module Shadows;
* A gradually-expanding star map.
Why did you have/make/use any of those maps?
In order:
* Because the encounter rules say to first roll for range of encounter. So I did. And then made up a description of the military installation that would make sense of the roll (from memory, it was a long-ish corridor). And then drew a picture of that with some doors that led to places that seemed to me to make sense in a military installation. I think at least one of the doors ending up mattering because NPCs holed up behind it. The map was drawn freehand on a bit of scrap paper, so was not particularly to scale but roughly represented the layout of the place.
* The PCs had been taken prisoner. Narration had established a compound with a yard where the prisoners had started, an interrogation room where they were interrogated, and a sick bay where they had been placed after being knocked unconscious during interrogation. When a PC in the yard escaped and entered the building, I drew a map (again, freehand on a bit of scrap paper) so that the player could see his options - eg he would have to walk past this doorway to get to the interrogation room (he knew it's location, having earlier been interrogated in it).
* I had a copy of the St Christopher map because nearly 40 years ago someone gave me a copy of Best of White Dwarf Adventure vol 2. When the PCs were taken prisoner in the St Christopher, using the map enabled me to show them where they were when they were taken into the vessel, and where they went when they were taken up to the bridge.
* I had a copy of the Annic Nova map because 20-odd years ago I bought a second-hand copy of Traveller Double Adventure no 1. When I decided to use the Annic Nova for my version of an Alien(s) scenario, I pulled out the map. Having it out on the table made it easy for me to tell the players where their PCs were in the vessel, and for them to say where they wanted their PCs to go.
* I had a copy of the alien installation map because Shadows is the other adventure in Double Adventure no 1. So when the PCs went to the ice world of Zinion to find a 2 billion year old alien installation, I decided to use the Shadows set up, suitably adapted. Using that map was the most exploration-heavy RPGing I've done for many years: the players declared actions for their PCs like going down a shaft or through a doorway, and I told them what their PCs saw. Having the map in the middle of the table also made it easy to point out to them where their PCs were in the facility.
* I am not using the standard Traveller technique for creating a star map (ie roll for each hex to see if it has a system). Rather, I have a table where I roll for the number of worlds within jump-1 of a given world. In the first session I established a series of worlds (that I had pre-rolled) at jump-1 distance because the PCs' ship was only jump-1 capable. Then I made a list of worlds and their jump distances from one another. Then when the list started getting a bit unwieldy I also converted it into a map which visually represents the jump distances. The action resolution rules for travelling from world to world are highly sensitive to the jump-distance between worlds, so a visual representation of that (together with my list that I still maintain) is helpful.
Why do you update the star map?
Because I make up new worlds. On the "edge" of the map are worlds with links to other worlds within jump-1 indicated (based on the roll I made on my table) but that I haven't rolled up yet because I haven't needed to.