The Daily Planet as the Hub would work, with a map you can open, showing you different sections of Metropolis that you can travel to. Random crimes are useless, since you're Superman, so I'd leave them out. At most, I'd have Superman stop crimes at the start of the game, to introduce you to the controls.
Areas should be restricted, with the illusion of a giant city, created through cinematic boss battles, that take the fight through several sections of Metropolis.
I believe the developers of the cancelled Superman game already had the right idea. Of course I don't know if whether or not they had a free-roaming environment in mind, but the cinematic battle with quicktime prompts looks amazing.
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And boss battles should allow for different outcomes, and paths you take can change, depending on how well you do during battles and quicktime events. Similar to Heavy Rain. A scenario with an enemy could end quickly if you managed to input the button commands correctly, or drag on if you messed up. So similar, the better you do during a fight, the safer the surroundings will be and you get the enemy away from civilians. Though if you mess up, you could crash into a total different section of the city, crash through a bridge support and would have to catch a train full with civilians.
And I'd love if they'd somehow made use of Superman's other abilities, like his superhearing, x-ray/telescope-vision, etc. The superhearing could be a mini-game similar to Arkham Asylum's high frequenzy lock picking. But instead of trying to match the frequency, you'd have to filter out noise till you hear what you're looking for. Like you can't find Lois, Jimmy, or whoever else, you listen to the surroundings, filter out the other sounds till you hear them shout for help, then a way pointer pops up showing you the way.