Can I sue the woman who hit my car here in the state where I am living or does it have to be done in the state where the accident happens?

For California, you have to sue where the accident took place or the defendant lives. The insurance company realizes that so is offering you a lower settlement amount. If you are suing for the decrease in value of your car [over and above of the cost of repair and a rental car at what it would actually cost you to rent], it will be very difficult to get any insurance company to pay. You need to get confirmation from 2-3 car dealers as to how much they would have to discount a car because of an accident.