As in, block-level organization.
The best ones start off as Neighborhood Watch-type. It can be informal (barbeque buddies shooting the bull, and deciding on organizing to keep an eye on the neighborhood. Those who need to walk a dog are likely recruits; they are out there already, and might as well make themselves useful.
In a SHTF situation, it will really pay off if you know your neighbors, who can be trusted, and – more importantly – who cannot. That information can save your life.
This post reminded me of all the reasons NOT to work with larger organizations.
Now, will neighboring groups occasionally interact? Sure. The Block Captains should have a working relationship with nearby groups. They can learn a lot about local government, common problems, and ways to improve life for their own neighborhood.
But, the main focus needs to be on those near to you.