I only spent a few hours in Las Vegas, NM, so I don’t have the best information but I can tell you a bit.
I ate lunch at Charlie’s Spic and Span. It’s a diner, nothing fancy, but you can get a decent GCCB.
A block or so away is Murphey’s Soda Fountain, although I’m not sure if it is still open… seemed on the verge of closing when I was there.
The town visitor’s center is in the railroad station, right next to an old Harvey hotel. Teddy Roosevelt stayed there during the Rough Rider reunions.
Be sure to visit Fort Union while you are there.