not sure on BBQ in Cary, or at least not Carolina style BBQ. There's Danny's over by Waverly Place that (at least IMO) is extremely underrated. There's also Dickey's and Remmington Grill not far from the Ale House or Buck's Billiards at Crossroads... at least I'm fairly sure both are at Crossroads, I know Remmington Grill is for sure. All 3 are more generic BBQ though, with Remmington and Dickey's both being chains either nationally or regionally. Don't think any of the 3 have TVs though.
I've been pleased with Danny's when I went to the one in Morrisville, which is closer to my part of Cary than Waverly.
Beyond that, I agree with DaveG that nothing else jumps to mind for Carolina style BBQ in Cary itself, especially south Cary. And nothing jumps to mind for a sports bar with Carolina style BBQ either. I know Carolina Ale House doesn't do pulled pork as a regular menu item; not sure about Tyler's.