Let's see.......
Superman: I'd have him operate out of Los Angeles. Since there's very few super heroes there, and the crime rate is spiking now that The Pride is gone, he'd become L.A.'s posterboy hero. This would, of course, lead to him having a tenuous relationship with the Runaways. His main enemies would be the Wrecking Crew, how would have set up shop in L.A. While they lack smarts, they certainly have the brute force to give Supes a threat. He'd eventually become the leader of a new West Coast Avengers.
Batman: You know, I'd pull a bit of a twist here. He's Bruce Wayne, a major buisnessman and playboy in New York. But, because there are so many crime fighters in New York already, one more would only complicate things. So, he begins finding vigilantes and funding them.
Wonder Woman: She'd apear as an ally of Ares. Much more cool headed and peacefull than Ares, but still a skilled and deadly warrior. She'd kill alot of Japanese demons. Yay.
Flash: He'd start off in the twin Kansas cities. Because of his speed, he quickly becomes an enemy of the now much crazier Quicksilver, who ends up in Kansas through his travels.
Green Lantern: Richard Rider restarts the Nova Corps. However, they're renamed the "Green Lantern" corps because they are to "light the way" in the now chaotic universe. Also, the slightly altered Nova Force has a green aura. One of his early recruits is Hal Jordan.
Aquaman: Namor's younger cousin, Orin. Much more cool headed than the current king of Atlantis, he serves as namor's tactical advisor. The two argue. Alot. Orin is also a mutant telepath.
Hawkman: Reincarnation of an Egyptian prince. Operates of of the New York Museum of History. Is kinda crazy.