To snag a ticket before they're gone or go up, your best bet is to peruse Google Flights (here's a sample search to get you started). At the time of this writing, the cheapest available roundtrip was on United in October for just $436, or roughly half of what it would normally cost.
Whether or not Singapore -- one of the world's best food cities -- is actually on your bucket list, or even on your "maybe" list, these flights are some of the cheapest you'll likely ever find from the contiguous US to Asia. And considering the storied city-state's proximity to places like Thailand and Malaysia, you could easily get to and from many other countries on the cheap, and turn your trip into one big Southeast Asian tour.
h/t The Points Guy