We used to have a thread about this, but for the life of me, I can't find it.
Honestly, the Superman Returns game had some good ideas. If it hadn't been rushed to fit the movie sales cycle, it might have turned out alright. They had the right idea by having a life bar for Metropolis. I would have gone a step further and had bars measuring the structural integrity of the various neighborhoods. Superman's weakness is that he can do anything but he can't do everything. So a good free-form Superman game would be about juggling a number of catastrophes at once and trying to keep the city intact. Maybe have the missions structured so each one takes place over the course of a day, and he has to juggle a variety of disasters. Maybe incorporate key points in the day where he needs to appear as Clark Kent to follow on story leads. There would have to be some sort of quick flight mechanism to jump to various hot spots on the map. Focus on the arcade nature, juggling combos strung together between enemies blocks from each other. Focus on frenetic action and high scores. I really think the "invulnerable Superman" thing wouldn't be too much of a problem. Conventional Earth weapons can't hurt Superman, but the majority of his threats are alien and high science concepts, and synthetic kryptonite, which is rather silly in comic books, would actually be a natural fit for later stages of a video game. Start by focusing on the city's health, and as the game progresses, present more enemies that could be a threat to Superman himself, so you have to balance the health of the city against Superman's life bar. Focus on large and epidemic threats, give it a good development time, and I think a sandbox style Superman game could be really cool.