In OTU terms our solar system is one system in a subsector (Subsector E or F of the Solomani Rim, I think - someone will no doubt correct me

) of a sector.
Sectors are made up of 16 subsectors arranged in a 4 x 4 grid, labeled A-P. Each subsetor is made up of a bunch of solar systems, and is mapped on the subsector form in the back of the main Traveller rulebook.
But, if you are creating your own background, stellar cartography can be done however you like. Hexes, grids, joined up "subway maps" - all sorts.
Personally, I like the traveller system of sectors and subsectors - it breaks things down nicely. I'd be inclined to think about a single subsector, and map that out. You can either randomly generate the systems as per the main rulebook, or, and this is the way I do it, think of the kind of planets you WANT your players to be adventuring on.
Look at films and books for inspiration. Think of the planets and cities in Starwars or Babylon 5 or Farscape or any of your favourite books, TV shows or films. Switch a few things around and you can come up with a variety of planets.
A couple of really useful things I've found is to try and sci-fi up things I'm familiar with. For instance, I work in the finiancial heart of London and travel on the tube (or subway to our colonial brothers) to work every day. I try to imagine what this would be like with anti-grav, holograms, super-materials and so on. Would the adverts be holographic? Would the train still jerk and make funny noises? woukld it it still stink of garbage and ozone?
The other one is a trick I picked up from a Star Wars GM guide. If you need a sci-fi name, look at the nearest book, flick to a random page and grab the last half of one word, and the first half of the next. Quick example - Illand Melc. Instant wierd sci-fi name!
G.