As I drive around, I see a lot of Delta 3-D deer and turkey targets in backyards all over the place, so i would assume that you could shoot your bow to practice in a safe and orderly manner. I do here in Allegheny Co., I stand in my neighbors back yard to take a 40yd shot with his permission of course.
But if you feel you need to know for sure I would call your local township or Borough to be sure.
As far as public land. I would think that if you abide by the 50yd. rule and set up your target in a safe manner you should be ok.
Bow and arrow, even a cross bow are a weapon but does not meet the definition of a firearm.
I have only seen regs about discharging a firearm.
Checking with the neighbors might be a good idea to avoid them calling on you but if your property is large enough to shoot safely in go to it.
I saw signs on developments stating no hunting on the property but again you are not hunting.
As said, this is typically governed by municipal ordinance. Go to your municipality's website and look through their ordinances, if available. Otherwise I would assume safety zones apply unless permission from neighbors is granted. Lastly, I wouldn't be too concerned with the municipal ordinances, you won't get in trouble unless somebody complains.
Before I moved to a home with a larger lot, I just put my target up against my house which had a cement block wall. If I missed the target the only thing that would happen is I would destroy an arrow. Baring any specific laws, I think as long as you can prove you are being safe, you should be able to talk your way out of any problems. IMHO
First thing you should to do is go down to your borough/township/City Hall and ask them if there are any ordinances against discharging a weapon with in your town. Also if you live in an HOA you may need to consult with the also. If you live out in the country and you don't have any neighbors close to you I would set a range up at home. If you not able to shoot at your home then you may want to look at the local and state ranges. Also do a search for a local Archery pro-shop and ask them where places to shoot are. Good Luck to you