A lot of the time you can lookup firearm ordinances on town websites since it's a commonly asked question. Many towns won't restrict it, some restrict it to certain areas, and some do not permit it at all inside the town limits.

Be aware of ricochets and your backdrop. Bullets can travel quite far if they skip off of hard ground. Soft berm backstop or equivalent to keep the projectiles from leaving your property if you're shooting anything in the rifle category. And, as always, shooting at a public or private range is preferred (though I too go shooting in my backyard sometimes; got to keep those property values down).

As courtesy, I'd be friendly and talk to nearby neighbors in hearing range to see if they have any times/dates they'd prefer you not shoot and see if you can accommodate them. I grew up next to an avid shooter; 90% of the time it wasn't an issue but sometimes they'd be going to town around dinner time and it's disruptive trying to watch TV/Movie while someone's dumping off 50 rounds half a mile away. It would have been nice if we could ask him to limit how much shooting they did past 5 pm or whatnot.