(covers information from an alternate timeline)
In 2268, the same Enterprise was detailed to transport delegates to the Babel Conference. A number of dignitaries lined the observation deck to see the reception of the Vulcan delegation. Later during that voyage, Ambassador Sarek made use of the observation deck for meditation. (TOS: "Journey to Babel")
In the 26th century of an alternate timeline, an observation deck aboard the USS Enterprise-J had a large window that showed a view of space. When Temporal Agent Daniels brought 22nd century Starfleet Captain Jonathan Archer through time to the Enterprise-J during the Battle of Procyon V, the observation deck was where they met. (ENT: "Azati Prime")
Background information Edit
The first on-screen reference to an "observation deck", in TOS: "The Conscience of the King", wasn't included in that episode's final revised draft script, whose stage directions instead notated it as being an "observation corridor".
The area aboard the Enterprise-J was consistently referred to as the ship's "observation deck" in the final draft script of "Azati Prime", though it is not given a name on screen. The script additionally described the area thus; "It's a long, narrow, platform-like room with large windows."
The observation deck of the Enterprise-J was designed by Set Designer Lee Cole, who later commented, "This set looks like a big graphic design because it has all these plant-on panels in very intricate designs and from different sources of inspiration." (Star Trek: Communicator issue 152, p. 43) The doors shown in the observation deck aboard the Enterprise-J appear to be the same used aboard Deep Space 9.
Scenic artist James Van Over contributed to the design of the Enterprise-J's observation deck by rendering some graphics. "We needed futuristic monitors, and Jim Van Over did some wonderful video for those," remembered Lee Cole. "I had circular monitor screens in different shapes, and when he put his stuff onto the television monitors it was quite a trick to get them to line up. But the finished product was amazing – his radiuses fit exactly inside my radiuses." (Star Trek: Communicator issue 152, p. 43)
Doug Drexler, who designed the exterior of the Enterprise-J, didn't approve of the look of its observation deck. He speculated it may actually have been built for Archer, just so he could relate to the interior of the vessel.