(covers information from several alternate timelines)
Early in her career, Ensign Ro served aboard the Wellington when the vessel visited Garon II, provoking an incident that would get her court martialed. This incident was noted in Ro's file in the crew manifest database for the USS Enterprise-D in 2368. (TNG: "Ensign Ro", "Conundrum")
In 2365, Captain Thomas Pucer was the commanding officer of this ship. In that year, the Wellington was assigned to patrol the Neutral Zone in Sector 130. The ship was named on the Starship Deploy Status chart in the Starbase 173 courtroom. (TNG: "The Measure Of A Man", okudagram)
In 2367, in the reality created by Beverly Crusher, the Wellington was in the same sector as Starbase 133. It reported no unusual readings after Wesley Crusher had performed warp field experiments aboard the Enterprise-D. (TNG: "Remember Me")
Background information Edit
The registry of the Wellington was derived from the chart in "The Measure Of A Man".
In an internal list of starships, dated 26 September 1990, the Wellington was classified as a Niagara-class starship and the registry was changed to NCC-28473.  This information would become the original source for the main Wellington entry found in the Star Trek Encyclopedia (4th ed., vol. 2, p. 483).
The first draft script for "11001001" called this ship the Washington.