Well, the five states with no sales tax are Alaska, Montana, New Hampshire, Oregon and Delaware, so no sales tax there.
Several states impose a small new tire fee, and most states have a small tire disposal fee, though.
In Indiana, just like when you enter your DOT number when buying fuel and are exempt from state tax, you get the same tax exemption when buying anything for the business, be it fuel, tires, parts, whatever. The same is true for Ohio and PA, where you provide the DOT number and the tire shop files the exemption form with the state. It's that way for most states. Call the tire shop and they'll know.