Welcome to the Midlands. Some good advice in here I'll expound on...
Hop Yard closed, but not necessarily because Matt had a kid, more so to pursue his own place, Cotton Town. He should be opening later this year. I was out at his hop farm for a gathering a few weeks back and man that guy knows his stuff and makes excellent beer. Matt is a tremendous resource and always willing to help other brewers out. The owner of Keg Cowboy was out at the hop farm as well, pretty sure they do not sell any homebrew stuff anymore.
BetMar on St. Andrews is almost your only option in the area. I get most of my grain from him, but still order my hops and yeast just because he usually doesn't have much variety when it comes to hops and yeast except the standards, e.g., US-05, Warrior, Mosaic, etc.
One more option (but in Cola, not Lex) is Bottles downtown near Garners Ferry and Rosewood intersection. It's a bottle shop (good selection) but they recently started carrying homebrew supplies. It's more equipment now, with some standard grains (no milling) and just started getting hops in, but no yeast.
As for beer and taprooms, check out Conquest and River Rat downtown near Williams-Brice (football stadium). IMO, Conquest makes better beer, but RR has a better atmosphere. RR is great to sit outside in the grass, they've got a nice deck, cornhole boards, all that jazz. Solid beer, just no wow factor. Conquest is in a warehouse and doesn't have much as far as ambiance goes, but the beer is good. They push the envelope a bit more than River Rat does.
Let me know if you ever want to get a beer or do some brewin!