"Next to" (or "beside") is just a simple preposition, lenk. The equivalent noun phrase ("the cat next to the box") would just be an myau lenk al piuleng.
When used with an object (rather than a location), pe means "in".
If you want to clarify or focus that the cat is inside the box, and not any other relation to it, you can add the word "tius".
A direction word can come directly after the preposition. With lenk "by", it means that the thing is close to the other thing and on the specified side.
A prepositional phrase starting with hu can come directly after a phrase talking about a direction (left or right, also up and down when talking about outer space) to indicate whose perspective this is from.
Hu hyangu specifies that the perspective being used is that of a map, oriented the way maps are usually oriented in this world (west = up).
Hu hyangu is a set phrase, so demonstratives, determiners, and other adjectives are not used with hyangu.
With the preposition pe "in, at", a direction specifies that the item is in that direction, but not necessarily close by.
This is similar; it uses sapchem as an adjective with its comparative form. Unlike the pe form, this only talks about one axis; that is, for example, the cat may also be far above the box or far in front of it.
...this also specifies that it's far away. (TODO is this right?)
This uses the adjective kalkel; using this adjective, the object being compared to is specified using the preposition hu.
Multiple direction-type words can be used together.
The word for "between" acts sort of like a conjunction, going between the two nouns.
Ípwenk usually refers to time, but it also has a metaphorical extension into space meaning "beyond"/"past".