And the winner is...
A many-way tie!
The time for this tie is "the end of time," also sometimes portrayed as "outside of time."
There are multiple movies and TV shows, as well as literature and video games, which depict things such as the end of time, the next universe after the end of time and then time restarts, post-time time has run out and now we are in a timeless 'place' where time is some singularity or nonexistent or other weird thing, and other variations of this theme.
All of these have in common that they are at the farthest extent of time or even beyond time, therefore they all tie for first place for this answer and none of them can be beaten.
Some examples have already been given: Hitchhiker's Guide to the Galaxy, Dr. Who, and Futurama.
In "Red Dwarf" season 5, episode 2 "The Inquisitor" the crew encounter an android who has lived to "the end of time." Once at the end of time, the android decides that there are no gods or afterlife, so the android builds a time machine and goes back to the past.
Another one is the TV series 12 Monkeys. 12 Monkeys had a cult which worshipped The Witness, a person who was born outside of time by two time travelers. Two time travelers conceived the child while in a temporary "pocket timeline," for lack of a better term, which was the result of their tampering with history and which should not have happened but did due to the many accumulating paradoxes. The traveler is worshipped as the one who lives outside time and who will bring an end to time. Although "outside time" does not always necessarily mean "after time," in this case the "outside time" quality is brought about through actions taken throughout history and it brings an end to time, so it is effectively "after all time."
There are also time-travel movies and shows in which people are trying to stop "the end of time" from becoming reality, but which I do not know enough about to know if anyone actually "goes there." Example: Quantum Break
These go beyond the scope of this question but are likely of interest to most people asking this question or reading it.
There are a lot of contenders if you were to include other story media such as literature and video games...
There was a video game, Chrono Trigger I think, in which you had to travel back and forth through time as part of the plot, with the farthest time being a place at "The End of Time" which used the concept "All time is spent and this is now a 'timeless' post-time place. Time is essentially frozen in place, though you can still move, talk, and perform other actions."
And there was a choose your own adventure book which involved a time-travel cave (go in one time, come out another exit at another time) which had a special "post-time" room as well which worked the same way.
In "The Time Traveler's Almanac" one of the time-traveling short stories had time-travel technology invented, and there was also an "end of time" there, but most people avoided it because nobody ever returned from it, so its properties are unknown to those in "normal time." Sorry, I do not recall the title of this short story.
In Dungeons and Dragons there is an elf-like race called the Le Shay. In at least the 3rd edition of D&D (not sure about other editions), the description of the immortal Le Shay suggests that they are already in such a situation relative to their home-time. Due to tampering with the universe, which produced a catastrophe that could not be fixed, the Le Shay managed to, somehow (they are secretive, so this part is unknown), get themselves beyond the end of time and into the next instance of a habitable timeline. So, if those rumors are to be believed, then the default setting is a "future" timeline that is beyond the end of time of a previous timeline. Also, D&D is available as movies and TV shows, however I am not aware if the Le Shay have made any appearances on the screen - I am only aware of their existence in literature, hence mentioning this in the special notes section.