I haven’t played the PC version, but I expect it’s the same as the console version: Prototype (from Activision in 2009; there’s another game listed with the same title). The story is utter garbage, but everything about the moment to moment gameplay is great, and it definitely checks the boxes you’re looking for. I never played the sequel, because it re-used the same map, and that’s a lot like playing a Mario game with all of the same levels as the one before it, but this first game rules.

If you have access to something that can play Xbox 360 games, I’d also highly recommend the first Crackdown.