If it was me, or if I was doing this on behalf of a client, I would go with an approach that was slightly more casual and a bit less direct (unless you have one specific house you really want).
Instead of door knocking, I'd spend some time in the area and talk to people when they're walking around (dog parks and playgrounds can be a great source to scope out information on a neighbourhood). Approach it with a casual attitude, express your love for "their" community and see if they give you any leads that you can then directly target. You don’t walk to be the “creepy guy stalking the playground”, but if you show a genuine interest in learning more about a community, people may be more receptive.
I'd also try talking to mail carriers and workers / owners in local establishments (more so anything that is family run like a diner or great breakfast spot vs. Starbucks) to see if they’ve heard any chatter about someone thinking of moving. This can also give you a great understanding of what it will be like to live in the area.
It’s been my experience that people don’t want to be solicited when they’re in the comfort of their own home. I have had much more success in taking a less direct approach, although it can take more of your time. You may get a different reaction then I would, because I’m a Realtor - people tend to put up their guard when they think you’re trying to sell them something.
As for mail outs, or leaving a letter in their mailbox, unless it’s specifically targeting the house, they may not take a generic flyer / letter too seriously.