"Let's hang out in Seoul tomorrow!"
Translation:내일 서울에서 놀아요!
Exactly. This is a location particle (not really preposition as it comes after the noun, not before).
The choice between 에 versus 에서 depends on the verb that follows. Action verbs (like this one) require 에서, "movement" (don't remember the exact terminology) verbs, like 가다, 오다, etc, require 에.
It means meet, not hang out. It just refers to the action. You could meet in Seoul and hang out in Busan.