CheapOair (and seemingly only them) currently have flights with Emirates (both legs on the A380) from New York (JFK) to Hong Kong (via Dubai) for just $347 return.
Hong Kong is a great destination in its own right, but it's also the Cathay Pacific hub – you can go to a lot of places with just 4,500 to 7,500 Avios one-way.
Sample dates are November 7 – 21 (this fare does not show up on ITA Matrix).
It is not clear which fare class it books into.
While I haven't booked yet, the 24-hour free cancellation is mandated by federal law – CheapOair should honor it.