You should use the address where you are currently living, especially if you don't know the address of the place where you are moving. The problem is, you will likely have to start a new policy once you move to Wyoming since each state has different insurance requirements. This also means that you will have to cancel your previous insurance policy and hope for a refund.
Car Insurance Costs
Our State of Insurance Report actually shows that the average premium in Wyoming of $1176 is below the nation average of $1323 per year. Since rates are partially based on the number of claims and damaging whether events in certain areas, it's possible that your rate is being impacted by things that are out of your control. If you recently filed a claim or were recently issued a ticket for a moving violation, that could also be why you're experience higher rates than before. The best way to find the lowest rate is to compare quotes with as many companies as possible.