A tidally locked planet

[Maraxus_]

I think the right map makes more sense. On the left, there is this outer rim of the map, that is actually very interesting to the setting and should not be split up, while on the right: Who needs details about the wastelands in the dayzone or the endless ice in the nightzone?

Two things that come into my mind: The day zone will be frozen over, if this has the base parameters like earth. Look at the north pole, it does no melt even in it's summer days, when the sun constantly shines on it at a low angle. When the sun does not shine at all, there should definitly be ice.

The dominant wind direction is easy: Air rises on the hot side and thus falls on the cold side and near the surface there will be a constant flow of air from night to day, thus the habitable rind will probably be a good bit towards the sunny side. Less "Land of the perpetual dawn" and more "Land of the perpetual 9 o'clock forenoon"

[Pixie]

This will generate a nice map/world. And I can imagine it will only allow for life on a marginal N-S strip, so the map projection fits perfectly. I'm curious to see where this goes.

The dominant wind direction is easy: Air rises on the hot side and thus falls on the cold side and near the surface there will be a constant flow of air from night to day, thus the habitable rind will probably be a good bit towards the sunny side. Less "Land of the perpetual dawn" and more "Land of the perpetual 9 o'clock forenoon"

... adding to Maraxus ...
Sea currents will be mighty and sea level will vary a lot in the planet, I reckon. Continuous heat on the lit side will not only evaporate a lot of water but also generate water bodies expansion on the sunny side. This, in turn, will generate a gravity fueled movement towards the dark side on all the oceans. On the other hand, very strong Dark->Lit winds will push the water surface forcing currents that bring icebergs into the light. Where these two contrary movements meet you will get perpetual rain and ubiquitous thunderstorms.
Furthermore, since the planet is rotating very slowly, Coriolis force might be negligible so the currents (sea or air) will be mainly dependent on the mountains/coast design and the region where they mix will tend to be the same and very well defined all the time.

(This is all guesswork, grounded, but guesswork...)