All of the recent Sci-Fi in movies and on TV inspired me to put together a Star Trek game. I decided to set it right after the end of Enterprise, or about 100 years before time of Kirk and Spock, when the Federation was just exploring beyond the local star systems. (this also puts it safely before the JJ Abrams timeline divergence. It is still not clear if the new series coming early next year will take place in the new timeline, or in Star Trek Classic.) This map is one I put together based on various sources, with plenty of blank space on the left, for the players to explore.
The hardest part is balancing an old school vibe with keeping things also canonical. I am a huge fan of the 1980s-2000s Star Trek series, that created a deep universe and political drama. But the classic series's pulpy vibe with its gunboat diplomacy, green-skinned dancing girls, and bizarre 60's psychedelic weirdness is pretty awesome too. So the map serves as the framework- where the numbered sectors contain the "serious" Star Trek universe, and there are trade agreements to solve and an evolving political arc. Meanwhile the unexplored zones indicated with a "Z" is the pulp-y space opera parts of the universe. I am treating the whole thing like a big sandbox for the players to have fun in, and they can choose which parts they are interested in exploring.
Each hex is 1 parsec, and may have one or more uninhabited M class star systems that are not shown. Only star systems that would be known at that time and are of K class or larger, are in habited, or are notable in some way are shown. I laid it out to printout on a 11x17 tabloid page, extending toward the frontier where the players will be spending their time. I may go back and make a larger 'square' version that extends evenly around the federation in all directions.
Here is a PDF version of the map that is better for printing. Feel free to use however you wish.