If the cited party in a car accident won't respond to the insurance agency, can I take them to small claims court?

You can sue the at-fault party for negligence.  Filing a lawsuit is your recourse since the other party is not responding.  You are the plaintiff.  The party you are suing is the defendant.  A lawsuit can be filed where the plaintiff lives or where the defendant lives or where the claim arose.

Your damages (the amount of compensation you are seeking in your lawsuit for negligence) would be the cost of repairs to your car.  If you need a rental car while your car is being repaired, the cost of the rental should also be included in your damages.

You will need to mitigate (minimize) damages by selecting a repair shop whose charges are comparable to other auto repair shops in the area.  If you were to select the most expensive repair shop you could find, your damages would be reduced accordingly.  You will also need to mitigate damages when selecting a rental car by selecting one with a reasonable rental rate.  If you were to select the most expensive rental you could find, your damages would be reduced accordingly.  Your damages in your Small Claims Court case should also include court costs.  Court costs would include the court filing fee and process server fee.