The last time I played, I found the most "engaging" thing to be trying to climb on rooftops and seeing how high I can jump down from with the double jump without dying. Not a long lasting excitement, but I'm kinda bored with the grind that the game otherwise is.
Do what I do. Run around to those little "crime scenes" you see all over the city. Hit one of the armed guys with cyberpsychosis, and watch as he off his buddies. Then hit him with suicide if cyberpsychosis wears off before he's done killing everyone.