Spinward Marches as their campaign's home sector and those who used the Solomani Rim, first published in 1982. I was a Spinward Marches man myself, in part because that's the sector GDW used in most of their earliest adventures and because that's the sector the older guys I knew also used. Even so, I found the Solomani Rim intriguing, especially as I became more and more enmeshed in the official Third Imperium setting.
For those of you unfamiliar with Traveller, the official setting postulates that humanity -- or "humaniti," as GDW spelled it -- originated on Earth (or Terra) and that 300,000 years in the past a mysterious race of aliens known only as the Ancients took members of the species to the stars as servants. Some of these other human races died out but some survived and prospered, three of whom discovered the ability to travel faster than light independently, one of which were the Terrans. In time, these humans came to be known as the Solomani, a coinage whose origin is never definitively explained, though most assumed it means "men of Sol." In any event, The Solomani Rim is a 48-page book written by John Harshman that details the sector of space dominated by the Solomani.
Like its predecessor, The Spinward Marches, The Solomani Rim describes all sixteen subsectors of the Solomani Rim sector using a two-page spread. On the left side are strings of alphanumeric entries that describe all the worlds of each subsector. I continue to be amazed both at my ability to remember just what these strings mean and how elegantly Marc Miller managed to condense so much information into so few characters. It remains one of the great hallmarks of Traveller that no other science fiction RPG has ever managed to provide so much information about a planet so succinctly. On the right side of the spread is a hex map that provides much of the same information graphically. Again, it's absolutely amazing that, back in 1977, Traveller did so much right that other roleplaying games continue to struggle with.
One of the things that separates The Solomani Rim from The Spinward Marches is a much clearer sense of place. By that, I mean that the Solomani Rim sector has a consistency and logic to it in terms of, for example, its naming conventions that suggests it's a real place with a real history. While the Marches has meaningless, "science fiction-y" world names like Rhylanor and Zamine and Roup, the Solomani Rim is filled with names like Barsoom and Krypton and Oz. It feels much more like a place that men from Earth had explored and colonized and that lends it a distinct appeal. Of course, The Solomani Rim also includes a lot more specific details about the history and culture of the sector than does The Spinward Marches.
By today's standards, these details aren't onerous -- maybe 6 pages of the whole -- but it's enough that, looking back, one can see that Traveller had changed a bit since the publication of The Spinward Marches in 1979. I don't remember thinking much of it at the time, since I was using the official Third Imperium setting anyway. Now, though, it becomes clear that, by 1982, Traveller had begun its inexorable shift away from being a generic sci-fi game of which the Third Imperium was but one sample setting to a sci-fi game about the Third Imperium. This is a shift that culminated in the publication of Traveller's second edition, the goofily named MegaTraveller in 1987, which "hardcoded" the Third Imperium into the rules in a way that the 1977 edition had not. It was perhaps an inevitable shift but it was a shift nonetheless and one that, I think, ultimately weakened the appeal of Traveller and contributed to its decline.