Hong Kong might actually work really well since it's one of the cheapest flights between LAX and the other half of the world. It wouldn't be a bad idea to do LAX - Sydney, hop around a bit, and then do Hong Kong - LAX. The key to doing a bunch of cities trip is figuring out where the cheap links are. For example, Sydney -> Sri Lanka is $1000. But Sydney -> Bangkok is $500 and Bangkok -> Sri Lanka is $140. With the $400 you just saved, you can have a very brilliant time in Bangkok! Say whaaaa?! flights.google.com's map feature is key.
I'd also check Kayak.com, it's where I found my tickets the cheapest. Find the most common business routes & hubs (Dubai, London, Frankfurt, HK, Singapore), they're often very cheap last-minute. Or find out where an airline has their main hub, it's often cheapest to fly there even if it's a detour.