A blended index averages across housing, food, transport, healthcare and utilities, but those don't move together. Housing is by far the biggest driver of differences between cities and varies enormously within a single metro — two neighborhoods twenty minutes apart can differ by 50%. Always price actual rentals or homes in the areas you'd realistically live.
Taxes deserve their own analysis. State income tax is the obvious one, and moving to a no-income-tax state can be worth a large effective raise. But those states often recover revenue through higher property or sales taxes, so a homeowner may see less benefit than a renter. Also weigh commute costs, whether you'd need a car, health insurance differences, and how the local job market affects your future options — a higher-cost city with far more opportunities can be worth a temporary squeeze.