Some of the links on this are out of date but you might check some of the events listed here: [NEW] Moon Guard Event Calendar
Pretty sure the Stonewind Storytelling event is still going and those can be a great way to learn a bit about other characters in the community, and make connections. Mekgrim mentioned the tavern night at the Wyvern’s Tale and the monthly guild expo. The Shadowsands Bazaar is a neutral cross-faction event (though not everyone there is neutral, it’s a neutral place where the more hot-headed among us keep our tempers in check) and the Elixir of Tongues you can get from that vendor in the Dalaran sewers allows x-faction communication, which helps tremendously): [Neutral RP Event] Shadow Sands Bazaar Lots of great connections to be made there.