As a Laredo native I can tell you that Laredo doesn't have a large sports bar scene.
However, their are great places to eat with large tvs:
-El Capataz: Great menu and one of the best bars. Classic cocktails with their own twist. Try the loaded fries, ceviche and dos equis mac. Cant go wrong with anything here!
-Cosmos: Food is always good and TVs!
-Hooters and Tilted Kilt: Although food is nothing special and is exactly what you expect. You cant beat the cold beer and the amount of TVs.
-Border Foundry: Aggie owned. If you're going to watch the Ags they will most likely be on the TV in the Patio or at the bar. Food is upscale and always great!
Saludos Brewing: Newer but have been twice their beer is great and have a couple TV options. They advertise NFL watch parties so they do expect a crowd to watch games.
Let me know if you got any questions about Laredo! The Laredo A&M Club is smaller but usually just puts on 2-3 events a year aside from Muster. If you want to get connected with them let me know!