Twitter said hello to New York City today as they opened their new East Coast headquarters at 340 Madison Avenue.

The brand new office will house 40 full-time employees, including engineers, designers and of course, advertising execs (it’s Madison Ave, right?)

New York is a big city for Twitter, with over 65 accounts being operated by the city government. Those accounts have over 300K followers. Mayor Michael Bloomberg is also active on Twitter, hosting Q&A sessions on the service using the #askmike hashtag. Recently, Twitter was the tool that the NYC government used to get out updates involving the situation with Hurricane Irene.

“We are proud to welcome Twitter to New York City’s growing technology sector,” Mike Bloomberg said. “New York City has always been a place where big ideas are born, and we are working to ensure it’s the place where the next great tech success story is written – from incubating dozens of start-up ventures to bringing a new Applied Sciences school here. Companies like Twitter provide us with an important way to engage with citizens, informing and serving them in real-time.”

Did you know that NYC has more Twitter users than anywhere else? Jack Dorsey lets us know –

“Twitter and New York share the same constant pulse of energy,” he said. “We’re looking forward to growing our presence in a city that has more Twitter users than any other city in the world and is led by innovators like Mayor Bloomberg who engage, inform and serve residents in realtime.”

So…Twitter and advertising? We’re guessing that the new Madison Avenue office location is not just a charming coincidence.

Here’s the press event featuring Jack Dorsey and Mayor Bloomberg –