Here is a list of ideas (by yours truly):
-Cop missions, make different storylines.
-Another fun thing to do is take the mask from "Three Leaf Clover" do robberies and all that.
-Explore, finding enterable buildings.
-Shootouts with the cops.
-Racing around Liberty (Brucie's Races)
-Making your own assassin's missions (Find an area, look for a certain car shootout the tires pull it to the side of the road and kill said target)
-You don't have to only have shootouts with cops, or play the storyline to have shootouts with gangs anymore. You can now go to certain locations to find gang locations (Story mode not multi). Here's the gang locations and how to verify them: http://www.gtaforums.com/index.php?showtopic=359178
, I recommend Chinatown, Alderney City and Hove Beach.
Hope I gave you and the other people reading this good ideas and fun things to do!