For example, did the Chinese and Norse use north as the direct up on their maps? Did any other cultures do this, and independently of each other?
If not, what cultures referred to south as up on their maps?
I can't speak to the cultures you specifically pointed out, but I will try and add something about Maya ideas of geography.
While the Maya didn't necessarily make maps that represented physical geography, they did make cosmological maps of the universe. The cardinal direction are very important ritually to the Maya in their conception of the "quadripartite universe".
East ("lak'in") is often assigned as the primary direction at the top of these cosmogram. East is also often the starting point for rituals which move to each cardinal direction as a station. This is largely due to the association of the East with the sun rising. Likewise, West is sometimes used as the primary direction. Again, for the association with the sunset. An example would be the cosmogram from the Madrid codex where the top of the page is labeled as West ("chik'in").
The Maya names for East and West both incorporate the word for sun, "k'in", emphasizing the importance of the solar cycle in combination with the direction.
Many Maya cities are oriented on an East-West axis rather than North-South. While this isn't a map exactly, it does reflect their conceptions about geography in the same way a map would.
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