I could tell you what *not* to do: don't refer to the directions and map at partners.uber.com . It's not quite accurate. LOOK at it, just don't follow the arrows and written instruction.
The rodeo was a taste different than Spurs games, and the setup for Spurs pickup/drop off seems to be more the norm. If you'd ever previously worked a Spurs game, ignore all the rest of this reply and go with what you know...
Still with me? Right: For pickup, go into Gate A, hang a right at the last entrance before you get to the toll booth going to the back area where the Sale Barns are. Stay to the RIGHT, as the left is reserved for taxis. Exit using the entrance for Gate B. Forget going R onto E Houston as you exit: you'll run into a barrier, and the traffic wrangler will yell at you and treat you like a doofus. Coca-Cola Place is the only way to go. At the end of that, you may go either R or L. Communicate with your pax and *TRY TO GET THEM TO MEET YOU AT FREEMAN COLISEUM*. 'Specially for a one-time event such as Garth Brooks, you are likely to have someone who's both new to Uber *and* has never done an outing to AT&T Center, and what a joy that will be for you. But, they'll tell you where they are or say they DON'T know where they are and try to get you to come to them. Don't bite, and don't try to navigate to their pin drop. You'll be sorry, your pax'll be mucho frustrated, and you'll have said traffic wranglers as well as other drivers hating the very sight of you. Oh...I didn't mention you'll start the trip late.
For dropoffs, enter at Gate B, head for the middle, and cut left when the road ends. You'll be in front of Freeman Coliseum, and will end up to the left side of that building. Let the traffic dude or babe know that you are Uber with a dropoff, and they'll feel fine. NOTE: You'll be in exactly that same lane or road I mentioned above for pickup. Exit using the entrance for Gate A.
Dunno whether I'll call it a shortcut, but for pickups, I use North New Braunfels from 35, then L onto E Houston Street. Gate A is the first gate you'll come to. If I'm downtown, E Houston is a straight shot to AT&T Center, natch. For pickups: AT&T Center Parkway, then R onto E Houston. Or, IH-10 to E Houston, but I doubt you'll be coming that way.
A tip that I offer to all newbies is to just do a dry run with your app offline, and watch where the taxis and limos go, and where the buses are parked. Make several trial runs if you need. Better to mess up and start over without a rider in the picture, and a mess up in heavy traffic with all those barriers in place can take up to 10 minutes to correct. I kid you not. Once you have the hang of it, switch on yer app, and Uber On!