We New Yorkers are a schizophrenic people. On one hand, we're fiercely independent; on the other, we love ourselves a community. (Just ask an Upper West Sider if she'd ever consider moving to the Lower East…)
Nextdoor makes it easy to connect like-minded folks by block.
Here's how it works: You sign up for the site or app and create a profile, then join or make new groups (say, with fellow parents in your building) to see a Facebook-style feed of what neighbors have to say or offer (like a reliable cat-sitter for those last-minute business trips). The city is already participating; it became an official partner to share relevant news, like extreme weather reports, which is especially handy since we seem to have hurricanes now.
If you see that your particular block is a little underrepresented, invite the folks you do know and build from there. The more you put in; the more you get out.
Now, it's important to note that it is still the Internet. But rest assured, it's secure. Every member's address is verified through a variety of ways and is never shown, nor shared.
The only thing you have to worry about is how much wine to buy for the next meet and greet.