I personally live in a neighborhood with a very strong and progressive neighborhood center. It has something for everybody. It's one of the reasons I moved to the neighborhood. Despite this huge advantage, on a smaller scale I held the first open house and invited all the neighbors on the block or bordering my yard over for a holiday party.
Then traffic got worse so we organized around getting a traffic circle. There were also the elderly neighbors we kept track of and offered to help with chores.
I think the best way is to figure out with a few people what needs to be done, who might like some help, or just figure out how to have inclusive fun! Nobody is best buds on our block, but I'll take my neighbor's dog who's locked up all day to the dog park when I go. I know they will do me a favor as well. I think paying it forward to decent people will start a trend!