I can't believe I'm saying this, but the Ultimate Spider-Man cartoon might have had the right idea in upgrading the Daily Bugle into "Daily Bugle Communications," a full-on news network where Jonah is constantly on TV screens in New York haranguing and calling out Spider-Man and other heroes.
All you'd need to do is find some way for Peter to be employed there, include Robbie, Betty, and some of the other Bugle reporters from the comics, and it would still work pretty much the same as it always has.