Depends on the city. Where I live, there is no law on the books regarding pellet guns within the city limits.
Yep, true. The police were called on me in Metairie, Louisiana for shooting the pellet gun.
But in Anderson, South Carolina, when I was 14 or so, you could walk around all day with a rifle on your shoulder and fire any weapon at all pretty much anywhere, and no one would even blink an eye. Average distance between houses was well over a mile.