The Galaxy
For cartographical simplification, the Milky Way has been divided up into four regions or Quadrants. The Federation, Cardassian Union, Bajor, Ferengi Alliance, Mulluran Empire and the bulk of known worlds are located in the Alpha Quadrant along with Serenity and the New Canada system. The Klingon and Romulan Empires are located within the Beta Quadrant. The remains of the Dominion are located in the Gamma Quadrant while the Borg infest the Delta Quadrant.
The Galaxy is almost unimaginably vast—only 24% of it has been charted and less than than thoroughly explored. Even the Alpha Quadrant is largely unknown, while the Gamma and Delta quadrants are almost untouched. The USS Voyager's flight across the Delta Quadrant revealed many secrets about this region's inhabitants, however, even the terraquads of information that have been relayed back to Starfleet Headquarters are only the smallest drop in the vast and unexplored sea of space that lies in this region. Likewise, the tragic events of the Dominion War have led to some information about the species and cultures in the Gamma Quadrant, but much exploration is left to be done.
The Federation and Its Neighbors
Serenity Colony and the New Canada system is located in the Alpha Quadrant, at the coreward-most extremity of Federation exploration limits. This is a section of space bordered on the coreward side by the G'kra Republic, on the spinward side by the former Mulluran Empire and Ferengi Alliance, on the rimward side by the Briar Patch Nebula, and on the anti-spinward side by open, unexplored space. This precarious position has put Serenity in a unique position—it is on a highly profitable trade route between G'kra and the Federation, uncomfortably near the front lines of continuing skirmishes with unfriendly empires, and teetering on the edge of the unexplored mass of the Galaxy.
Trans-Briar Patch Sectors
The New Canada system is on the very edge of Federation space, within 1 lightyear of the edge of the Briar Patch, and less than 20 lightyears from the former Mulluran border. Most of the star systems surrounding the New Canada system are still being explored.
With the Second Mulluran War finally at an end, and the G'kra Republic the newest member of the Federation, Serenity's focus has changed from a highly-militarized footing to encompass Starfleet's original goals of exploration and discovery. Scientific missions are launched and supplied through Serenity Spaceport and the orbiting supply depot, and every day new information about unexplored space filters back to Serenity Colony.
The New Canada System
New Canada is a single-star system consisting of a type G7 V star—slightly smaller and cooler than Earth's sun, Sol. new Canada is orbited by five major planetary bodies, three large planetoids, and innumerable asteroids concentrated in one major belt.