Probably not worth a lot of your time and money unless the ticket is extremely high. I would just talk to the restaurant.
My standard disclaimer: I am not offering legal advice, assume I do not know the law in your state and that I am just making suggestions for starting points for when you do speak with an attorney. Do NOT rely on anything I write and contact a lawyer in your area immediately after reading my posting.
If the vehicle is registered in your name, you are the responsible party unless you can provide the Court with the information of who was 'operating' the vehicle at that time.
Most parking tickets have a nominal fine and do not involve any collateral consequences. When a client gets one, I usually recommend they do a cost/benefit analysis to determine whether the cost of the defense and the time they will spend in Court is worth the price they will pay if they just pay the ticket. Obviously, this is not true if the car was parked in a very resticted space like 'Handicapped Only Parking.'
You may get a prosecutor and/or the judge to cut you some slack if they have seen this type of situation occur regularly around that restaurant. If not, costs? /benefits?
This answer does not, nor is it intended to, create an attorney-client relationship or constitute attorney advertising. Rather, it is offered solely for information purposes. Since the facts of each case are different, it is critical to consult with qualified counsel with whom information can be shared and assessed under an attorney-client privilege, so that competent advice can be obtained on which you can make informed decisions.