The Assassination Mod lets you contact a mysterious contractor using public payphones.
There are a few other noteworthy script mods that give you more to do in Liberty City. Their AI exceeds follower AI in a lot of big budget releases (*cough* Skyrim *cough*) in that they'll seek out vehicles and follow you and follow you if you drive off on your own. It'll cost a bit of money, but once they're in your employ they'll follow you until you fire them (with F7).
Once installed, press F3 to command a pedestrian to join your cause. Recruit passers by, give them guns and roll through the streets as one almighty posse using the Bodyguard recruiter mod.
