A map from the Tax Foundation showing how each state taxes Social Security benefits. Some states (shown in purple) rely on the federal calculation of the taxable portion of Social Security benefits. States shown in blue do not tax Social Security benefits, even if those benefits are taxed at the federal level. Some states do not tax income at all (shown in green) and so do not tax Social Security benefits. And eight states (shown in yellow) tax Social Security benefits in some other way, such as using income or age to determine the taxable portion of benefits.
For more details, see "Monday Map: State Income Taxes on Social Security Benefits" (Tax Foundation).