We live in a quiet suburban neighborhood, and so far I have taught six of my kids to be safe and independent while playing outside without me. IMO, the most important thing is traffic safety. Always check before entering the street. Never cross from behind a parked car. Always walk on the sidewalk if possible, or if you have to walk in the street, walk AGAINST traffic. Always ride your bike WITH traffic. Never bike or walk in the street while wearing headphones. Always assume that there IS a car coming, and they CAN'T see you. Always be alert.
Traffic is the most significant danger that any child faces while out and about, and it deserves the most attention.
I don't teach my kids to inherently fear strangers. Not only do FBI crime statistics prove that "stranger danger" was faulty, I need to know that my kids feel confident asking for help if they need it. I also feel it's important for them to develop a sense of intuition to let them know if a situation feels "off," and they can't do that if they find every interaction with unknown adults scary. Lastly, I think the best protection is for every adult in the neighborhood to know my kids and to feel confident stepping in if something seems wrong to them. Too many adults are scared to step in, lest they look like the bad guy. So I teach my kids to be friendly and outgoing. Just never get into a car with anyone, or go into anyone's house, or go off with anyone without my explicit permission, from my mouth. Not just "strangers," anyone. If someone needs help, refer them to me. If a situation feels creepy or makes you uncomfortable, remove yourself immediately and either come home or find safe adults and ask for help. If you have a problem that you can't handle on your own, either come home or find safe adults and ask for help.
Unfortunately, I have also had to teach my kids how to deal with bored, busybody police. Some people don't like homeschooling, and some people don't like that I let my kids play outside without me, and think that my parenting decisions are a matter for the police. Sometimes the cops just take it on themselves, like the one who used to sit on the corner by our house and nitpick every single thing the neighborhood children did. He used to get mad at pre-teens for playing ball in the street on a quiet sidestreet of our quiet suburban neighborhood. Once he brought my daughter home and yelled at me because she was walking on the curb. Another time he tried to stop my daughter from walking two houses down to see her friend -- when her friend's dad was standing right there waiting for her. Dad gave the cop a good chewing out over that one. So I have taught my children to be polite to the police, but to refuse to answer any questions except name and address, and to refer everything else to me. They're only supposed to say, "You need to ask my mom about that. You can find her at [our address]."