I don't think you'll find a "good" answer.
Lots of cycling going on implies lots of people, which is Dallas, Plano, places like that.
"Riding to the grocery store" works great for me here in Garland, which is part of the DFW metromess. It just depends on where the stores are in relation to your house, and I can get to two or three different stores via mainly alleys and bike trails. That's not to say it's some sort of cycling Nirvana.
Lots of places may have good cycling and NO grocery store, the folks just drive 20 miles to the next town for groceries.
In a lot of places, if you want to do lots of cycling, your best option is a gravel bike and go seek out gravel roads.
Alpine is not that large, but actually has some cycling going on (college town) and has enough hills in the area to be interesting. We rode through on our recent Big Bend tour.
I've got friends that run a bike shop in Sherman, but they like gravel riding.
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