Strange phenomena are staples of fantasy and SF, especially when the latter involves explorations of the cosmos. Space offers nebulas, radiation, and alien planet environments. We can invent all manner of experiences that have no real explanation or at best, pseudoscience to impart believability or specific effects on characters and their environment, such as an interstellar ship. Space phenomena have a great advantage in that their location is flexible; we can place them wherever we feel like it and invent them on the fly.
By contrast, singularities on a planet or other body (moon, asteroid, etc.) are typically associated with a given location. They often benefit from at least speculation as to their causes. Technological or magical disasters, resulting from experiments or battle, offer easy rationalizations and even suggest world figures or famous items that might’ve been involved. Monsters or creatures can be a result, too. Does this phenomenon influence only things that come in contact with it or can it affect nearby objects? Maybe it can compel people to approach.
We can also create seemingly unrelated phenomena in different locations but which bear some similarities, but later associate them with each other. We might also have phenomena that begat other phenomena, with no one knowing this until characters stumble upon the truth. This sort of layering adds depth while fascinating audiences as oddities they’ve experienced before are revealed to have new significance.
There might be places where magic or technology doesn’t work, is unpredictable, or is supercharged. Animals could go wild, which is a cliché, or become docile if we want a new impact. There can be locations allowing extraordinary travel, whether actual doorways, random spots, or the former built on the latter. These gateways can lead to other physical locations, supernatural ones, or an alternate reality or timeline. These methods may be predictable, controllable, or neither. Can only certain people or devices activate them? Or we can have a portal open constantly because no one knows how to close it. Beings could be summoned through them.
On Earth, we have places where strange behavior is believed to occur, like the Bermuda Triangle or crop circles. Then there’s Area 51, a rumored place for storing unusual items. The origins of places like Stonehenge or Easter Island have been debated, but we can invent similar locations and attribute fantastic reasons for their existence.