To me Traveller, published by GDW Games and now by Mongoose, is one of the best sci-fi games ever published. One of the things that appealed to me was the star system generation rules and it's ability to create a universe as big as you want. It gives you just enough information to run a sandbox sci-fi campaign. What Traveller doesn't do is tell you how to manage all this information to run a successful game.
I am going to assume you are creating your own background although some of this applies to the 3rd Imperium as well.
Roll up two Subsectors side by side.
Note all the high population planets.
Write a short paragraph on each High Population Plant placing them in the context of your background (Empire, Federation, Free Space, etc).
Find any high tech plants (the highest ones you rolled )
Make one paragraph notes on them.
Find all class A and B starports
Make notes on them.
Each of the three levels of note taking will get progressively shorter as there is considerable overlap.
Scan the remaining plants.
Pick out 4 to 8 that grab your attention.
Make notes on them.
Look at your notes and come up with two to four "plots" that ties one or more locales together. For example a pirate fleet that uses one planet as a base, one planet for shore leave, and two other planets that they raid on a continual basis.
For each of the planets that you have made notes for, write up four "patron" encounters for each. They should start as one sentence each and be self contained in respect to the major plots.
Come up with 6 to 12 general patron encounters that can be placed anywhere in your setting. Make them flexible like (set in a seedy starport, etc)
Make up a rumor chart with 10 to 20 items that feeds information about the plots you came up with and the setting.
Make a list of NPCs. Assign them to the various items you created above. Start out with a sentance worth of info for each.
Look at your notes and decided where recurring NPCs will be. (Captain of the subsector Revenue Patrol, Custom Offical, Badger the Broker, etc). Probably need 6 to 12 of them. Give them a paragraph description in addition to their stats.
This should take about four evenings of Prep for two sub sectors probably two to three evenings for a single subsector. Each subsequent subsector will be slightly less time to prepare as you can reuse elements.
After your first adventure evaluate the players actions and decide if any sites will be needed for the next session. Prepare them in whatever level of detail you normally do.
Traveller is VERY amicable to the use of Computer Software to generate many aspects of the game. In the 80s on a TRS-80 I would make printouts of a hundred random entries of every type (subsectors, animal encounters, NPCs, etc). Then I would scan the list and pick out the ones I would be using.
Whatever you do don't just accept the first thing that pops out. Relying on totally random results will lead to nonsense. The Traveller Charts are good but not that good.
The point of all this is to make a "kit" that you can use to pull out whatever you need. This way you don't have to spend a lot of time in prep. Once the kit is formed then running Traveller is pretty much responding to whatever your players do.