We can tell you what state has the least registration fees and taxes however you will need to be resident of the state where you want to plate your vehicle since that is where your registration and taxes will be paid out for the vehicle as well.
We have read from sources such as Kiplinger that Oregon is the cheapest state in which to register a car. Residents of Oregon do not have sales tax so that automatically makes it cheaper than most all states to put tags on a vehicle.
According to the Oregon DMV to register a vehicle you must pay title fees, registration fees and license plate fees. The regular title fee is $55, vehicle registration fees for a new vehicle are $108 for 5 years then renewals (which are for 2 years) would cost $54. Two plates cost $5. So that is $168 for registering a vehicle for the first time there.
Another state without sales tax is Alaska so their registration and plate fees are also known to be cheaper than most states. The state that is typically the most expensive to plate a car is Nevada which can run a car owner around $2000 over 5 years. This state even charges a government services tax.
Kiplinger.com has an article dedicated to about the tax friendly places to a car where they give information on the costs to vehicle owners in all 50 states. There are some states that levy a vehicle tax year after year. Most states charge a sales tax in year one plus title and registration charges and, if applicable, plate fees, lien fees and emission fees.
This information may help you find out the states in which it is cheaper to register and plate a vehicle however as we mentioned earlier you will need to live a state normally to tag it there. You cannot simply choose a state in which to plate a vehicle and go there because when you return back to your home state you would usually be required to then register and tag it there.
To find out what the fees are to register and tag a vehicle in the state in which you reside contact your Department of Motor Vehicles.