Map courtesy of Star Trek Star Charts:  The Complete Atlas of Star Trek by Geoffrey Mandel; October 8, 2002; ISBN 10 - 0743437705; ISBN 13 - 978-0743437707

Federation space is located approximately thirty thousand light years from the core of the galaxy, on the border of the Alpha and Beta Quadrants within the Orion Arm. By 2267, its territory had expanded across a thousand planets, spanning 8000 light years within interstellar space. This included the territories of at least 150 member worlds, with thousands of colonies and outposts, a vast expanse of uninhabited space, and planets inhabited by pre-warp civilizations which are directly incorporated under the political jurisdiction of Federation space as of 2370. Entering within Federation space has jurisdiction implications: possible health and safety inspections, enforcement of the Prime Directive, as well as certain goods being banned (Romulan ale for example).