Edge of the universe

The edge of the universe was the location where space actually ended, beyond which there was nothing but the Black Void.

Mondas was said to have drifted to "the edge of space". (TV: The Tenth Planet)

The Empress of the Racnoss travelled to the edge of the universe in her Webstar, where she hibernated until the Secret Heart was uncovered. (TV: The Runaway Bride)

The Dæmon Azal travelled to the edge of the universe in the spacecraft Leviathan, where he encountered and merged with his counterpart from another reality. (COMIC: Voyage to the Edge of the Universe)

According to Salamar, Zeta Minor was located "on the very edge of the known universe." (TV: Planet of Evil)

The Fourth Doctor and Leela travelled to the "edge of the cosmos", where they detected the R1C's ion drive and encountered a spiral nebula. (TV: Underworld)

The Fourth Doctor, Mike Yates and Fenella Wibbsey travelled to the edge of the universe, where the Demon had create the Sepulchre atop a planetoid. (AUDIO: Sepulchre)

In 1999, Anne Travers banished the Great Intelligence, stranding it on the edges of the universe, riding the blue shift outwards into infinity. (PROSE: Millennial Rites)

fled from the Krotons to the edge of the universe, where he collected the exotic particles he needed for use against the Chronovores. (PROSE: The Quantum Archangel)

The Monk travelled to the edge of the universe, where he summoned Artemis. (PROSE: No Future)

The Eighth Doctor and Molly O'Sullivan travelled to the edge of the universe, where they encountered Liv Chenka and the Eminence. (AUDIO: Time's Horizon)

The Time Lords existed at "the end of the universe, give or take a star system", having moved Gallifrey there for protection when they emerged from the pocket universe the Doctor had placed it in. Further on, at five minutes before "Hell", Me was found by the Twelfth Doctor, waiting in the Cloisters in the bowels of the Capitol for the end of the universe. In her own words, she had been watching the stars die to pass the time until the end. However, she eventually left with Clara Oswald to drop the Doctor off in Nevada, and then to take Clara back to Gallifrey "the long way round." (TV: Hell Bent)

Behind the scenes
In the real world, the universe doesn't have an edge because space is curved.