You are rarely going to ever have any law enforcement jack with you shooting a target with your bow in the city unless it is an unsafe situation. They have better things to do but if the property is not yours and your shooting on private land it could pose a problem like trespass. You do not have to have an archery stamp or license to shoot at a target. Most guys I know practice in their backyard and they do not have ten acres.  Cinnamon creek  ranch just opened the largest 3d range in Texas out by Cabelas try there it is awesome.  www.cinnamoncreekranch.com

I have been shooting on the side of my house inside city limits for the past 3 yearsat least three times a week.  Residential neighborhood, made a backstop out of some hay bales, plus the fence behind that.  Never thought anything about it, and none of the neighbors complained.  Then, about a month ago, an officer just happened to drive by during one of my practice sessions and informed me that it was considered "discharging a weapon inside city limits", and yes it is illegal.

city limits is a big part of the answer - every city has different rules

if you are outside of city limits, I have not seen a county that prevents you from shooting a bow in a safe manner.

You can get arrested for recklessly driving your lawnmower. Safe use of backstop, etc., matters.

The "discharge of a firearm" doesn't apply from my conversations with Sherrifs - which I have asked several times this question.