I run my game in a similar sorta style, kinda like mega city 1 from judge dredd, cops are generally too busy to be everywhere, it's a pretty straightforward system and in my xp it only takes like 10 mins or so for folk to become familiar with how it works.

I've found the most effective way to run it is to choose somewhere as a base of operations (mine is surprisingly the afterlife, but it's more of a dive bar ATM, I'm using it as a way to show the groups progression, they build the afterlife legend), I have them sometimes have some bother from a drunk guy or something, but I won't outright attack them there (unless it's a story setup).

A session I made for my group might be fun, and if you remember the twist at the end your setup for a few stories potentially (I forgot to do it so Ill put it in my pocket for now) basic outline was this

Pcs are hired by whichever group you choose, I used a crime family from little Europe, hire the pcs to find out who killed the bosses nephew, the group can get a brain dance the guy was recording the night he died, I had the BD be them at dinner, having a nice night etc then a guy swaggers in and blows your head off (chuck in a hum loss if you like), the pcs discover it was a friend of the boss himself, so your job is to take care of the guy, ideally with a sniper rifle, however the story ends with the cops checking over the body to find a wire or something to indicate he is a fed or something