United has round-trip flights from Houston (IAH) to Sydney (SYD) for 75,000 miles/points, NONSTOP. 37.5k miles/points each way. Regular economy, not basic. Fare allows for carry-on bag and seat selection. Flights in February and March.
Booking flights with miles/points is worthwhile when the cost of airfare is high.
The best way to put together a round-trip itinerary with United points would be to look at both one-way calendars and then write down the available dates that have the lowest point redemptions, then plug those dates into a separate round-trip search to book. See links to calendar provided on our webpage. A laptop or a real computer will be easier to search with than a phone browser, this is because the United mobile calendar sucks, it removes fare details when the displaying the calendar.







