The first area after you leave the plaza in the Gutter is Entertainment District I. The one after that, to the "north" is II. It's the one after the first batch of fighting.
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So you know the plaza, right? The place with Mahir's place, the jobs, the crate you stand on? You exit that going "North"/Up. Then you fight your way through the next section, the one with the middle path you can't use yet, and kinda snake around till you're at the top and exit there. The map you end up on, the one where you either collapse or meet Mahir once you're out on the street, is Ent. Dist. II.