I'm in NYC metro. Goals are things you can score goals through. Hockey, soccer, field hockey, lacrosse (I think) have goals. Football has goal posts, but not goals because nothing stops the ball in the back and you don't score a goal, you score a field goal.
Basketball hoops contain nets. Hoops are hung on backboards. If someone draws lines on their driveway, it's a court or half court. If they just have the hoop, we'd say that. We might also say net because some folks have a hoop with no net, but if there's a net there must be a hoop.
If you say goal to me, you're in the wrong sport. I mean, a lot of readers would be confused by that in a picture book. If you're writing a character from KY for an audience from KY, go for the goal.