You may be able to get insurance in one state if you have unpaid traffic violations in another state IF your license has not been suspended due to the unpaid tickets in the first state.
In most states if you do not pay tickets then your license and/or vehicle's registration will be suspended until the traffic tickets are properly paid or otherwise taken care of. You would then need to both take care of the ticket and get your license reinstated so that you could legally drive and also acquire insurance for your car.
For example in Massachusetts traffic tickets, even including unpaid parking tickets, can prevent you from renewing your license or vehicle registration. Without having a full valid license it will be difficult to obtain insurance in your same state or a different state. Also keep in mind that many states have extra fees for reinstating your license or vehicle registration.
To keep your license from being suspended it is usually best to either pay a traffic ticket or fight it in court. Some states allow you to defer adjudication or take traffic school in order to take care of the ticket and keep it off of your driving record. So if it is the conviction of the traffic ticket affecting your driver's history you may want to see if you can get the ticket reduced or taken care of in such a way that your driving record is not affected.
If the tickets you received are not in your home state keep in mind that most states are members of both the Drivers License Compact (DLC) and Non-Resident Violator Compact (NRVC).
With the DLC, member states report back moving violations convictions back to the home state of the driver. The NRVC allows member states to suspend the driver's license of those who get traffic tickets for moving violations in other states and fail to pay them. So even if you received the ticket out of state do not assume that your license cannot be suspended in your home state if you fail to pay the ticket.
If your license is not suspended due to unpaid tickets in your state or out of state then normally you can obtain insurance. To get an auto insurance quote follow this link.