(covers information from several alternate timelines)
In the 22nd century, there was a powerful astrometric computer located in San Francisco. When Klaang was kidnapped from Enterprise NX-01 in 2151, Sub-Commander T'Pol suggested returning to Earth to make use of the computer in analyzing a spatial distortion registered by Enterprise's sensors. (ENT: "Broken Bow")
Later that year, an astrometrics lab aboard the Vulcan civilian transport Vahklas was used by T'Pol and Tolaris to study the Arachnid Nebula. The room contained a small statue of Surak, even though the ship was a V'tosh ka'tur vessel, and figured into a dream T'Pol experienced during the ship's visit to the nebula. (ENT: "Fusion")
Enterprise NX-01 had an astrometrics section. In 2153, while preparing to survey a hypergiant, Captain Archer noted that astrometrics must be "chomping at the bit" to start their studies. While secretly visiting the cogenitor Charles aboard a Vissian starship, working in the astrometrics lab was one cover story that Commander Charles "Trip" Tucker told the Vissians aboard the ship. (ENT: "Cogenitor")
One particular example was the astrometrics lab on the USS Voyager, which was designed by Ensign Harry Kim and Seven of Nine. Incorporating Borg technology, it could measure the radiation of up to three billion stars simultaneously, resulting in readings ten times more accurate than was previously possible. Astrometrics was used for charting stars, planets, nebulae, and other stellar bodies. It contained a large, wraparound, holographic wall screen which could display a stellar region three-dimensionally. There were a series of control panels to manipulate the screen. The area below the screen and in front of the control panels could be used as a stage during presentations. Astrometrics also included three workstations on the side wall. The lab became Seven's primary workspace, where she mapped and catalogued interstellar bodies which the ship encountered. (VOY: "Year of Hell")
For convenience or advanced analysis, astrometrics could also be used for communications purposes or even as a workplace for easy access to sensor information. Astrometrics was used by the crew of Voyager to communicate with Earth, once contact was established through the Pathfinder Project.
In 2375, when Seven suffered a type of multiple personality disorder, she took on the persona of Ferengi DaiMon Torrot and offered Captain Janeway twenty bars of latinum for the large astrometrics screen. (VOY: "Infinite Regress")
The USS Enterprise-E was equipped with an astrometrics lab in which a direct link with Starfleet Cartography could be established. Interference from nearby astronomical phenomena (such as the Bassen Rift) could interfere with the lab's link with Starfleet Cartography. Lieutenant Commander Data utilized the lab to plot the Enterprise's rendezvous with Star Fleet Battle Group Omega in 2379. (Star Trek Nemesis)