I havn't used Dragonstar yet (waiting for second core rulebook to come out), but I have a list of adventure ideas I've seen here and there.
Description from official site: Intrepid adventurers explore the Outlands in starships powered by fusion fire and arcane rituals. Dwarven prospectors work veins of pure adamantine in remote asteroid belts, and elven loremasters conduct secret experiments in living space stations. Grizzled mercenaries augment their bodies with bioengineered spellware, and orc raiders armed with pulse lasers massacre innocent settlers on isolated colony worlds.
Free adventure from official site: Prisoners of Aphex, a free Dragonstar adventure module written by Wil Upchurch. This scenario takes the PCs and their mysterious Drow prisoner to Aphex, a remote outworld whose only tie to the Empire is a small, isolated prison whose guards and inmates are all but forgotten. Once there they find that the prisoners have rioted and the guards have sealed themselves into a small control room, safe from whatever menace has broken free in the prison's medical wing. Can the characters unravel the mysteries surrounding the prison, or will they themselves become prisoners of Aphex?
List of convetion adventures off the official site:
Evacuation of Mistral
The city of New Ghemenskol is one of two outposts of technology on Mistral. Only twenty years after the arrival of the Empire the bombs are falling again, only this time there is no demand for surrender, and no way to stop the invasion.
Legacy of the Lost World
En route to Thordin's Belt, the characters intercept a destress signal from a ship orbiting an uncharted planet. When they investigate the derelict vessel, they find themselves caught up in the events that could decide the outcome of the invasion of the Rimward Barrens
Throdin's Belt
Thordin's Secret
The characters confront an ancient secret hidden in the heart of Thordin's Belt.
The War Within
The characters make unexpected allies and face hidden dangers as they are caught up in the Imperial response to the invasion of the Rimward Barrens
The Price of Betrayal
The characters find themselves in the center of a conspiracy that threatens to tear the Empire apart.
I've also noticed mention in these enworld boards of the exploration of a mining asteroid.