Of course you're able to greet people in your neighborhood, because you're either in a setting you're familiar with, or with people you know. In either case, there's nothing to give you that sense of pressure, so, it's easier for you to say "Hi" to them. Now, being in an area that you're not familiar with, that's where greeting people matter, ladies in this case, because it forces you to get your brain pumping to form those sentences out of nowhere. Think of giving a speach in speach class for the first time: IT'S UTTERLY NERVE WRACKING to those who're not use to speaking to crowds of people. I remember when I went up for my speach. The moment I stared into the crowd, my mind went blank and I kept uttering those retarded verbal pauses "um...", "err...", "ah..", list goes on. We choke like this because we really worry about how your audience will accept you such as: "I wonder if they'll think I'll suck...I don't want them to think that!", or "What if i choke, I could never live that down!".
Same thing happens when you meet some arbitrary girl you like: your brain seems to shut down when you need it most and you don't know what to say to save your life, or the conversation with this girl in this case! Some men torture themselves with doubt and regection since that's what they're already expecting, so, they'll just simply walk by the lady without even trying! Who knows, maybe that particular lady would've actually liked that guy, but he'll never know since he never bothered to open his mouth. Just don't worry too much about talking to ladies you don't know. Do know that the more you do this, the easier it will become because you'll be desensitized at some point, hopefully. Make eye contact, greet, and try at conversation. I know you've heard this DOZENS of times but talking about something obvious in your surrounding, or the current situation, is a good ice breaker to get a conversation started with a complete stranger. Remember to smile when you talk, KEEP eye contact, and watch her body language. DO NOT keep most of the conversational topic on you, your accomplishments, or whatever it is that might lead to bragging since this bores most ladies. Ask questions about how she's feeling, how her day went, or try to look for something about her that makes her unique...within reason. Trust me, if she's into you, she'll either talk your ear off, or blush the whole time you're listening to her WITH YOUR EYES TO HERS. That's the other thing, if you get this feeling about some girl you're approaching and you attempt to make simple eye contact as your smiling, DON'T BE THE FIRST TO LOOK AWAY. Make sure that it's the lady that looks away first. I gaurantee you, you'll immediately know if there's the slightest hint of interest in her depending on how she reacts to you! If she either folds her arms, or turns both her head AND body away from you, that's a good sign that she's not interested and you'll most likely be rejected...even though most persistant guys still try anyway.
Girls also pay attention to little things that most men aren't aware of such as: your hands, finger nails, hair, eyes, clothing, posture, facial expressions, yadda-yadda, etc. Just keep yourself clean & tidy, also your clothes, do not slouch around since most women look at that as low self-esteem, even though you might not be. And when you do talk to a lady out of the blue, do not cross your legs, fold your arms, or look away because this'll passively tell the lady that you won't open up to her and you're not interested in her in that way...more body language. In the middle of conversation, if she starts to brush her hair behind her ears, takes little pauses from conversation to look at you, closes the space between you two by leaning towards you while she keeps her arms unfolded, or touches you playfully after a joke, SHE'S INTERESTED!
It frustrates me so when guys miss out on those signs since they continuously dwell of the thought of rejection...what's the worst that can happen to you? What, she'll just say "no, sorry", or something close that. Dude, I don't care who tells you otherwise, YOU'RE GOING TO BE REJECTED! Just don't lose face, and try again. Think of it this way: most "assholes" you see who call themselves "players" do get a lot of women, but ask them if most of those "dates" were worth investing in. I'd rather date a handful of women in my life and have MEANINGFUL relationships to grow and learn from, than to date all the women I could possibly nab just to be a so-called "man", cause in the end, you won't have anything meaningful. ...Alright, I rambled on again, but I think you get the picture. Hope I was able to help you, Flymop! Go out there and make it happen!
Gah this is really a sore topic for me, I'm just gonna stay away from this one, sorry. 
