Just for a moment of relevance (I'll get over it, no doubt) there's a little FATE-system RPG called Diaspora that has a good system for generating star clusters that could certainly be adapted for Battletech use.
Let's say, for example, we're creating a little group of 5 star systems off in the Periphery. Because I'm an unoriginal hack we'll call them Arcadia, Babylon, Circe, Dagda and Eden.
The systems are each rated on Technology, Environment and Resources, using a FATE dice roll (4 dice, each providing +1/0/-1, or 4(d3-2) if that's easier). You then roll for each to see where the interstellar links are - or for this purpose, which systems are within 1 jump of each other.
Arcadia - T0 E-1 R-2 - links to Babylon
Babylon - T1 E-1 R-1 - links to Arcadia, Circe, Dagda, Eden
Circe - T2 E3 R2 - links to Babylon, Dagda
Dagda - T1 E0 R2 - links to Babylon, Circe, Eden
Eden - T0 E-3 R0 - links to Babylon, Dagda
Arcadia
Arcadia is a backwater, impoverished world, which retains a breathable atmosphere and biosphere only in deep canyons. Although it has little contact with the rest of the cluster it's a home for isolationist groups and dissenters from other systems. Many small communities hide between canyon walls and the tradition of asking no questions makes it a frequent place for criminals to hide out or carry out discreet deals. The harsh conditions wipe out unprepared settlers and some inhabitants encourage that along, living on what they can loot from derelict towns.
Babylon
Babylon has a single hostile world, with a belt of blisteringly hot desert separating tropical polar regions habitable by humanity. However it's the trading hub for the cluster, accessible in a single jump from any of the other worlds and can build dropships. It has to tax trade through it to pay Circe for new jumpships and repairs to their older vessels. The southern polar states are satrapies of Circe while the northern pole favours Dagda and proxy battles are fought there. The leaders of both poles collude to keep the war simmering to prevent Circe and Dagda from reducing restrictions on trading directly and cutting Babylon out of the cluster's economy entirely.
Circe
The most advanced system in the cluster, Circe is incredibly wealthy with two worlds that were colonised without any need for colonisation and substantial germanium deposits. Circe has developed the capability to build jumpships, albeit at a primitive level, which may prove the decisive factor in their long-running rivalry with Dagda. Ostensibly democratic, Circe is dominated by a hundred or so political and economic dynasties that control 90% of the system's wealth.
Dagda
The other centre of human population in the cluster, Dagda itself is as rich as either of Circe's worlds but its technology lags behind. Like Babylon it has a dropship fleet but it relies on reconditioned ships from the old colonial expedition for interstellar trade. Fortunately it has the lion's share of these, as the first world settled in the cluster. Autocratic nobles control fiefs on Dagda, united under the rule of a monarch elected for life from their ranks.
Eden
Domed cities exist on Eden's one populated world. Once it was a lovely world but unrestricted nuclear and chemical warfare has reduced it to fractious city-states buried beneath glass and granite. Wars are fought between the cities using fusion-powered tanks and 'Mechs. During periods of peace many of these soldiers wind up as mercenaries fighting proxy wars on Babylon.