Below a certain size, a town just isn't going to have a grocery store or a hardware store at all.

Because I live in central Texas, my knowledge of what's out there is biased toward that. Kerrville was the first town I thought of that might meet your criteria. It's near some of the prettiest country in the state, and I've done a lot of riding on the farm-to-market roads around there. But yeah, the main drag is a highway through town, and either you reconcile yourself to that or you look somewhere else. It's close enough to Austin and San Antonio that you've got reasonable access to airports and other big-city amenities. It has its own real hospital (something else that is vanishing from small town in Texas). I'd be surprised if there were one inch of bike lanes in town, but there is a pretty good bike store.

Alpine is extremely remote, but it's in another one of my favorite parts of Texas. The nearest major city would be El Paso. Again, it's a big enough town to be self-contained in terms of urban amenities.

San Marcos is a small city with a fairly large student population. Its downtown is very accessible for cyclists and pedestrians. Increasingly, Austin (and to a lesser extent San Antonio) are encroaching on it, and I would not be surprised to see it become a bedroom community for Austin.