There is no such thing as a tax-free state. The ones that have no income tax typically have a property tax rate twice as high as others. Most states also have sales tax approaching 10%. Some states have personal property taxes, most often on vehicles, boats, etc. Also, as they say, you get what you pay for. Taxes are very low in Arkansas, Mississippi, and Alabama, but there is a reason for this. Are you retired or near it? Most states exempt Social Security, and some exempt all or part of certain pensions and IRA income.
Nashville is nice. I love Carson City. Haven't been to San Antonio, but it's supposed to be a bit like San Diego, only with a river.
There is a lot of affordable area in the midwest. We followed our son to Indiana, and bought a perfectly adequate 2000-sf house for $199k. Taxes are about $2200 on that. We don't have kids; the schools are not great; the teachers are underpaid. One thing different here from crowded urban areas is that there may be 100 miles between major cities. This is actually good, as it causes a city of 100k people to have every kind of store you want, good health care, and maybe a university. In between, it's quiet and rural, and if that suits you, great -- but if you want a nice library, music venues, a nearby hospital of any repute, and more than a few restaurants, you might find it wanting.
There are even less expensive real estate areas in Pennsylvania, Michigan, Ohio and some parts of Kentucky, for example. But worse weather.
Other than real estate, and in some places gasoline and utilities, most places are about the same.
Much more important is the environment and weather. Look at temperature extremes (Nashville is OK) and tornado belts (Nashville is semi-OK on that one). We ended up in Evansville two years ago, and we were surprised to find that so far the winters are not bad -- usually above 20 degrees, maybe four snows, not more than 4-5 inches at a time, although worse have happened -- and the summers can be 90 degrees and 75% humidity, but we were actually expecting wetter. Summer nights are MUCH warmer than in the west -- maybe 72. Don't like that much. Spring and fall are beautiful. Visit first, or monitor the weather on Wunderground. Or sign up as a pet-sitter and come visit for free (DM me).