im no desk top lawyer but i believe the last i checked, the law says it is illegal to hunt, doesnt say anything about practice or discharge of a bow. also check to see if you are in the 50 yard law. 150 yards from occ. dwellings in most places but some are 50 now i think.
Those are hunting specs. Target shooting is presumed to have a safe backstop to prevent any strays leaving your property.(If any do leave your property prepare for enormous legal issues) again your county,town,community may have it's own rules. As long as your neighbors are ok with it you should be ok with bow or airguns. The only change to byf43's recomendation would be to make it portable so your HOA does'nt ding you for a permanent "eyesore".