your honor, it's his zodiac sign

One of the biggest departures from their more traditional depictions of the usual Batman cast was that of Caped Crusader's version of the Riddler, thus named in-universe because he "riddles" everything with blunts (although he does at least once do the usual riddle/joke schtick).

While a large departure from most versions of the character, Caped Crusader's Eddie is actually intended to be a specific meta joke, which like a lot of stuff in season two, kinda relies on the audience's familiarity with early/mid-century crime cinema (or at least the curiousity to look it up afterwards).

In this case, Eddie's appearance, personality and trigger-happy violence is intended as a reference to the character Tommy Udo, as played by Richard Widmark in the 1947 film noir Kiss of Death...

...With Widmark's performance as Udo being a key inspiration for Frank Gorshin's depiction of the Riddler in the 1960s live-action Batman show with Adam West.

So, rather than being entirely random, Caped Crusader's version of the Riddler is instead a call-back to the inspiration of an earlier version of the character rather than, say, the Batman drawing parallels with the Zodiac Killer or something.

Because it's a massive East Coast city but the property values are probably like $200 a month for a three bedroom apartment, and most Gothamites are like, "Hey, Bane never swore to break my back."

And here's the thing: you're not just moving out of Gotham City. You're moving into the rest of the DC universe. And it has hero-based power scaling.

Oh, Metropolis looks fucking great. But it gets invaded by aliens and robots and demigods, because Superman is there.

Wonder Woman's tangling with gods.

You go to Central City, and some Reverse-Flash motherfucker runs backwards from an alternate future and kicks your balls off at the speed of light.

You could move to the West Coast, and oh, an entire city just gets exploded by Cyborg Superman or some shit.

How about you move to Indianapolis, or Cleveland? Haha, no. They have no protector during the alien invasions, and you're in Cleveland

So stay in Gotham. Sure, you have lunatics, but you know that if you had a gun, you at least have a chance against the Joker or Riddler. Mongo of War-World would crush you. But Gotham just has creeps, and you know you have a chance. Even Bane, R'as Al-Ghul, Killer Croc, and Mr. Freeze are just slightly altered dudes. Oh no, Poison Ivy is going to kiss me to death! Who gives a shit, you kinda wanted to go out that way anyway.

I think it's all about perception. Gotham City has crime. But when Ares sends his undying legions to march upon the mortal realm and Wonder Woman has to punch all of them, people don't internalize that as "crime." That's "a crisis" or "a religious event" or at best, terrorism. Same thing when Superman has to stop Brainiac from shrinking Metropolis or whatever. That stuff is objectively more dangerous but it's on such a huge scale that "crime" is not the word for it. The cops don't involve themselves in this at any point. But the stuff Batman deals with is like, robberies, assaults, gang wars, serial killings. All his villains commit actual crimes, so they go into police reports, which end up as statistics. So when someone compiles all this data, oh look, Gotham City has the highest crime rate in the country, yet again. Forget the fact that 10% of Keystone City's population had their skulls crushed by invading superintelligent gorillas. Who cares that a random guy in Opal City accidentally teleported the entire state to Hell after he found out the hard way that he was born a wizard. Those are not crimes. There's nothing in the police recordkeeping app's drop-down menu for a Gorilla invasion. Closest thing we've got is Random Chimp Event.