Multiple realities
(covers information from several alternate timelines)
Honeymoon on Andoris

Ritterhouse's "Honeymoon on Andoris" drawing

A honeymoon, an Earth ritual, is the traditional trip taken by a newlywed couple to celebrate their marriage, and presumably, consummate it.

The song "Come Fly with Me", a favorite tune of Vic Fontaine's, featured the lyrics, "You just say the words, and we'll beat the birds down to Acapulco Bay; It's perfect, for a flying honeymoon – they say...." (DS9: "His Way")

On the Taresian homeworld, the women native to that planet infect alien males with a retrovirus that transform them into male Taresians. The newly transformed males then marry three of the Taresian women. On their honeymoon, the women then kill the male for his genetic material. (VOY: "Favorite Son")

In 1947, Faith Garland's mother suggested that she and her fiancé, Jeff Carlson, visit Niagara Falls for their honeymoon. (DS9: "Little Green Men")

In an alternate timeline, Commander Charles Tucker III and Sub-Commander T'Pol had their honeymoon in cargo bay 3 of Enterprise NX-01, which Tucker filled with sand they dug up from a passing asteroid and decorated with a palm tree that he had manufactured himself. (ENT: "")

Roy Ritterhouse created an artwork entitled "Honeymoon on Andoris" for the science fiction magazine Incredible Tales, intended to spur on the development of a short story. (DS9: "Far Beyond the Stars")

In 2369, "honeymoon" was a word which appeared on a medical analysis, seen by Doctor Julian Bashir, who was infected by the aphasia virus at the time. (DS9: "Babel")

Also that year, new USS Enterprise-D Captain Edward Jellico noted to Deanna Troi that he didn't have time for a honeymoon with the crew (a period of getting to know and understand the crew), so she would have to see to their morale. (TNG: "Chain of Command")

In 2374, Worf proposed that he and Jadzia Dax undertake a hiking trip across Vulcan's Forge for their honeymoon, or possibly venture on a mountain climbing expedition on Andor. Dax rejected the ideas as entailing too much suffering. Jadzia instead consulted the Starfleet Bureau of Information in locating a more suitable planet. She wound up finding and suggesting Casperia Prime, to which Worf finally conceded. (DS9: "Change of Heart")

A cut scene from "Strange Bedfellows" had Kasidy Yates also consider the Mountains of Andoria as a site for her honeymoon with Benjamin Sisko after the Dominion War.
Paris-Torres honeymoon

The Delta Flyer II during Tom Paris' and B'Elanna Torres' honeymoon

Michael Eddington and Rebecca Sullivan were never able to take a honeymoon, as Eddington was captured by Starfleet and later killed by the Jem'Hadar. (DS9: "Blaze of Glory")

In 2375, during the wedding of the biomimetic duplicates of Tom Paris and B'Elanna Torres, the duplicate of Captain Kathryn Janeway stated that Torres had asked her to forego the rigors of Klingon painstiks in favor of a more traditional ceremony. This led the duplicate of Harry Kim to quip that they were saving the painstiks for the honeymoon. Later, as Torres investigated a strange phenomenon which was affecting the duplicate USS Voyager, she commented "I guess the honeymoon's off." Later, before she succumbed to radiation poisoning, the biomimetic Paris told the duplicate Torres he had already selected a place for their honeymoon: the Graystone Hotel. Showing her an isolinear chip programmed for the holodeck, he described lovingly the details, which included a drive in a vintage Duesenberg and dancing the Charleston in a genuine speakeasy, but watched in horror as she passed away before his eyes. (VOY: "Course: Oblivion")

After using it to participate in a stellar race, the real Tom Paris and B'Elanna Torres took the Delta Flyer out for their honeymoon. (VOY: "Drive")

In 2379, William T. Riker and Deanna Troi planned on having their honeymoon at the Opal Sea on Betazed. Their honeymoon, however, was delayed when the USS Enterprise-E was diverted to Romulus, while en route to Betazed. (Star Trek Nemesis)

In the writers' second draft script of ENT: "Breaking the Ice", Travis Mayweather criticized Malcolm Reed's supposedly unsentimental attitude, while they were preparing to visit Archer's Comet, by pointing out that Reed was packing a munitions case as though he was "headed for a honeymoon in Vegas." Reed explained the highly prepared nature of his packing was a result of him being wary about the risks of visiting the comet.
In dialogue that was included in the shooting script for Star Trek Nemesis but not in the final version of that film, Worf was to have explained to Riker and Troi that a traditional Klingon honeymoon starts with "the Kholamar desert march," involving endurance trials in which the couple bonds, and that, if the couple survives that challenge, they proceed to the Fire Caves of Fek'lhr to confront the demons of Gre'thor.