At this point, you should just try to remember where stuff is.A map will just become an inconvenience since it'd be a map outside of the game. Also, in-game, if you open the map and zoom in onto your character, the game will reveal lootable object locations within the proximity of where you are.
I pretty much burned an image in my head of where things are, depending on where I spawn in. FDR and Broadway, for example. Broadway is the ultimate goal before I enter into the dark zone if I spawn on the left, FDR is where I run to immediately if I spawn in Stuyvesant, and from there, I travel north west.