exempt plates doesn't mean no insurance it means it does not have to take emissions tests. city garbage trucks have insurance through the city, just like the police department and the fire department.
anyways, what you do is take it to a repair shop. you get absolutely everything that could have possibly happened during this accident priced for fixing. then you take the quote to the city building and hand it to them. if they have a preferred shop then you may have to go to the preferred shop. anyways you did get a accident report done by the police right? if not its going to be a pain in your *** if the driver wants to lie and say it didn't happen.
so whatever the amount of damage it did to your vehicle is. they will have to cut a check for that price. its the city so they will cut it pretty quick. if it is an option i would suggest you have the bumper replaced and repainted, and the quarter panel will probably have to be banged out, epoxied, and repainted.
shops can only make quart sizes of paint for repaints which is about 300-500 dollars or so. plus they have to pay for the Mitsubishi paint color code as well. if the rear bumper has to be replaced it can cost about 700 dollars just for a new OEM bumper. and the body work can cost about 400 bucks depending on how long it takes the body guy to fix the damage. price may range from 1100-1600 depending on the body shop you go to.
i suggest you take your car to a few (4-5) shops and get price quotes remember the least expensive shops price, taking it to a privately owned shop tends to be pricier so if your looking for the big bucks (from the city) go to one of those. then take it to the cheaper shop to have the work done. also remember that an after market bumper will cost less than an OEM bumper new, and buying a salvage yard bumper will be the least expensive.
http://www.car-part.com for that
sorry the post was so long