At some point in the mid-2360s, the starship USS Thomas Paine was assigned to a diplomatic mission to Alderaan, according to a Starfleet report titled Starship mission status. (TNG: "Brothers", et al.)
Information on this planet was from Okudagrams. According to the reference book "Star Trek Chronology", in the "A" section of the locations index, this planet was listed as, "Never visited by the crew of the USS Enterprise-D."
The reference to this planet, as well as the wording of several Okudagrams, was an in-joke. Alderaan was, of course, the adopted homeworld of Star Wars's Princess Leia, who claimed to be on a diplomatic mission to Alderaan when captured by Darth Vader in the opening scene of Star Wars.
The name of this planet originally also appeared in "Up The Long Ladder", on an Okudagram on Picard's desk monitor as the destination of HMS New Zealand in 2135. A legible version of the original okudagram appeared in the reference book, Star Trek: The Next Generation - The Continuing Mission. In the remastered version of the episode, the planet was renamed as Aldebaran.
Prior to 2151, Earth ships had been operating within 90 light years of the Sol system. In that year, the Enterprise became the first ship to travel further than this distance. If the reference had been kept in "Up The Long Ladder", with the diplomatic mission to this world in 2135, Alderaan would probably have been located within this range. (ENT: "Two Days and Two Nights")