"Business is bad, I need to concentrate on upmarket cars. I'm sick of people writing me off as a two-bit joke. Get me a Jefferson Provincial please."
You will be taking this car from the Diamond Motors dealership in Little Italy. There will be two guards watching it but they're hardly a threat and put up little resistance so take them out however you see fit.
Once they're taken care of, pick the car's lock because, as Joe Barbaro would say, "Beautiful car like that, it'd be a shame to smash the window." Besides, you get paid more if the car is undamaged.
Once you're inside drive it to the garage in South Millville. There's plenty of time on the clock so there's no hurry, plus you won't get a chance to drive this car at any other time in this DLC. When you get to the garage park under the rotating 'P' icon to end the mission.