Saints Rows the third

I'd definitely suggest trying the second one, it has it's own charms, including a zombie survival mini game which is awesome

The activities really make the game i think, a few examples:

Insurance Fraud
Objective: Throw yourself into harm’s way to earn cash and respect.
The basics are simple: use the trigger buttons to dive in front of oncoming traffic. The more you bounce around, the higher the medical bills.

Septic Avenger
Objective: Spray sewage all over your targets to earn cash and respect.

Just exploring this game and doing all the activities is massive fun, the story isn't half bad either.