I don't think you will likely be able to fully establish an anarchist community without influence of the state, but here are some things that are jumping off points from actual projects of varying proximity to anarchy/ism.
I had a friend involved in the Albany, NY Free School, and while I don't think it is an explicitly anarchist project, there were some initiatives that grew up around it (cooperative housing, community gardens, etc.) that would appeal to anarchists. Coincidentally, there was a strong amount of action opposing the gentrification of the city at the same time.
Similarly, in Tacoma, WA the Catholic Workers at one time owned most of the houses on a block and had torn down the fences in the back yeard and built a community garden that was shared with other residents of the neighborhood. They also provided housing to folks transitioning out of prison and/or homelessness, and hosted events in support of other radical projects, though their connection to explicit anarchists is tenuous at best.
Community gardens ain't anarchy. I've never lived in Albany, so I don't feel up to really trying to assess the efficacy of that project, though my impression is that more and more the school and the autonomous initiatives that sprung up around it became selling points for why that part of Albany was so nice and so appealing to move in to if you were a young urban hipster starting a family. Tacoma is closer to me geographically, but I am still well removed from them. I get the impression that they are carrying on with their holy work, but are basically maintaining their grasp on the hilltop, but that that grasp is slipping the more that money comes in to Tacoma.
For other models, I would suggest looking at what has happened in some college towns, where anarchists have been able to carve a niche for themselves, though most often only a temporary one. There are also examples from outside the US like Exarchia in Greece which it might be of interest to study, but what is really important is recognizing context.
A few neighbors who want to have an anarchist community can do a lot, but if other neighbors don't want to have an anarchist community and decide to call the cops, that all means shit. I have nver been involved in a successful geographically based anarchist community (as opposed to a scene) like you are seemingly wanting, but my suspicion is that patience and knowing when to be invisible are really important. I also think probably also being able to balance that with holding to the fierce anger and the destructive side of anarchism, or else you will become just a tea society.
