If you'd want to start a "club" - try reddit, or facebook. Else as previously suggested, what you're talking about sounds alarmingly like the regional "chapters" for which there is a suitable section on this forum. Possibly the "off-topic" or "general discussion" area might also be suitable.
Traditionally, Embassies are hosted in the capital city of the hosting nation, and form the "head offices" of diplomatic missions. They are very much official. The obvious problem here is gaining permission to establish an embassy - something that is expected to be easier once the UN recognises us officially as a nation, although not assured on a nation-by-nation basis.
Outside of the nations capital, it's common to additionally have "consulates" - these are more akin to "regional offices" and typically deal with individual persons and businesses - and represent the most commonly used service. The barriers to establishing an embassy are equal to that of establishing a consulate, but if you can score one the other is pretty much assured.
An unofficial physical place - despite being practically useless - could be easily be established. If you don't want to stick a sign in your front yard and have hoards of people trapsing thorugh your house, rent out a town hall or similar facilities.