Here are more tips...
When scheduling a date, always make it in a public place. Do not let them know where you live before or after the date. Don't have them ring your doorbell and pick you up, meet them at the place wherever you're going. I live in NYC like you do, and I often like to meet guys in my neighborhood so it's just easier to get home, but I am always vague about which street I live on. I say I live a few blocks away or something, even when we're just around the corner from my apartment. If they want to walk me to my door, I generally tell them that's not necessary. If someone insists, I will stop in front of a different building from my own to say goodnight (preferably a doorman building so the guy has a sense of being watched) and then make sure they leave before I walk to my actual door. If I'm meeting someone in a neighborhood other than my own, I just make sure it's somewhere easy to get a cab, or where there are plenty of restaurants and/or doorman buildings around in case I need to "escape" somewhere to feel safe.
Sometimes there is chemistry on a date, but if there is any making out, I still try not to do it in front of my building.
Oh, and usually I prefer to make coffee dates, or to meet for cocktails (and have no more than two drinks). Don't let yourself get drunk on a new first date, and try not to make lunch or dinner dates simply because that means you'll be stuck with them for the length of a meal if you're not getting along, or they're boring or unattractive.
Here's some advice a friend gave me and I'm glad she did, because I was able to use it and it felt incredibly liberating: If a date isn't going well, or you're disappointed, do not feel obligated to stay. You can opt to leave at any time, even if he's ordered dinner. Life is too short to sit at a table wishing you were somewhere else. I used to think I had to stay "until the date was over," not realizing I can say it's over whenever I want! The first time I did it was about 30 minutes into the date. It wasn't just that I didn't find him attractive and we were not hitting it off - he was also a nut job! Not a dangerous type, just... nuts. The waiter had come over to see if we wanted another drink and I said, "No thanks." My date said, "Do you want to go somewhere else?" I told him, "No, I'm going to go home." He then asked me, "What, no sparks?" and I answered, "Nope, sorry, no sparks. But it was nice to meet you. Have a good night" And I paid for my wine and left. From now on, I will never make myself endure another bad date for an entire evening when it's so simple just to leave.
If I don't want to see someone again, sometimes I will email the guy afterwards with a message like, "Thank you for coffee. I enjoyed our conversation but I don't think we're a match. I wish you the best." I usually do that asap to nip any hope in the bud. Sometimes my intuition tells me not to even bother, and usually that turns out that they don't contact me again either, so we were on the same page. If I do want to see them again, I email them and say somethng nice and charming, but without sounding too hopeful. But that is trickier and depends on the person.
The world opens up... when you do.
Oh, oh, can't you see? Love is the drug for me. ~Bryan Ferry
"Love is that condition in which another person's happiness is essential to your own." ~Robert Heinlein