Obligatory mention of Sleeping Dogs, if you haven't played it then get on that! Fantastic story, gorgeous graphics (even the "old" version) the ability to parkour around, and Batman: Arkham style combat.
The city itself has plenty of things to do, tons of races to take part in, fight clubs, the ability to buy cars/motorcycles, plenty of clothing stores selling a range of clothing styles, the ability to buy food from street vendors, clubs to find and sing karaoke in, and random events like chasing down purse thieves or escorting a drunk away from a store, just to name a few activities.
I know some people were disappointed by the lack of gunplay (it's there, but fairly rare) but the hand to hand combat is absolutely fun and has a lot of depth, and there is just something amazing about being able to lock a enemy into the trunk of a car. I actually did that the other day, free roamed for a while, found three thugs hanging out in a parking lot, so I shoved each of them into a car trunk.