It is generally considered unsafe to eat wild rabbit until after the first hard frost due to tularemia. If you do harvest wild rabbit, pay close attention to the internal organs and discard any meat where the internal organs are discolored or spotted. Also, pay close attention to the tick/flea load on the animal. At least, that is widespread country wisdom around these parts, YMMV.
Conies, while they aren't a 'meat breed' and don't have much meat on them are delicious. My dog agrees. According to her, the head is the tastiest part.
I'm not sure where you live but I'd think twice (and probably still do it) about eating rabbit from anywhere where people routinely put pesticides on their lawns.
I've always been a bit curious -- you cook the rabbit. Which pesticides (etc) survive the cooking process to the point where you'd need to worry about them?
Most pesticides survive the cooking process. As a rule of thumb, cooking kills most biological baddies (bacteria, worms, etc) and doesn't do much for anything else. If your threat model includes pesticides, botulinum toxin, or a number of other contaminations then you probably need to just avoid that food source, or at least limit exposure.
Urban gardens are a thing. Urban squirrel isn't recommended for the menu.