I suggest that you "hang around" the Yard if you've never been to USNA (or not been there often), you don't want to walk/drive back and forth, you want to socialize with other parents, you want to shop in the MidStore, and/or you want to learn more about what PS and USNA will be like for your mid (for those who may not have a lot of knowledge).
I agree you should not stay to "spy on" or hope to catch a glimpse of your child during the day (between reporting and the time with families at the end of the day). For you, it smacks of being a helicopter parent. For your mid . . . it's downright embarrassing. Remember a lot of parents can't afford to (or otherwise can't) come at all. This is the first step in letting go. Don't be one of "those parents," especially in front of your kid. Let go.