Australia and New Zealand from the U.S.

Sydney

Points System Economy Premium Economy Business Class First Class Airlines You Fly On Stopover Transfer Partners
Virgin Atlantic from LAX 60,000N/A90.000N/AAir New ZealandNoMarriott, Amex, Chase, and Citi
Alaska 80,00095,000110,000140,000Qantas is cheapest for Business or First; Cathay Pacific, Fiji, KoreanYes (One)Marriott
ANA70,000N/A115,000210,000ANA (Star Alliance for 5-15k more points)Yes (One)Marriott and American Express
Cathay Pacific (LAX)60,00072,000120,000180,000Cathay Pacific or Japan AirlinesYes (Two)Marriott, Amex, and Citi
Japan Airlines 90,000N/A120,000170,000American Airlines or Qantas (Direct Flights)Yes (One)Marriott
Etihad75,000N/A125,000145,000American (ANA for more)NoMarriott and American Express
Lufthansa80,000N/A135,000210,000Air Canada, Air China, ANA, Asiana, EVA, Singapore, and United.Yes (Two)Marriott
Cathay Pacific (NYC)90,000108,000145,000220,000Cathay Pacific or Japan AirlinesYes (Two)Marriott, Amex, and Citi
United80,000N/A160,000200,000United (Partners more expensive)Yes (One)Marriott and Chase
American80,000N/A160,000220,000American, JAL, or Cathay PacificNoMarriott
Aeroplan/Air Canada90,000N/A160,000220,000Air Canada, Air China, ANA, Asiana, EVA, Singapore, and United.Yes (One)Amex and Marriott
LifeMiles/Avianca 80,000N/A160,000222,000Air Canada, Air China, ANA, Asiana, EVA, Singapore, and United.NoCiti and Marriott
Asiana110,000N/A165,000240,000Asiana (Partners Extra)Yes (Seoul)Marriott
Korean Airlines110,000N/A185,000260,000Korean Air. (Partners cost more)Yes (2 on Korean)Marriott and Chase
Singapore Airlines (LAX)110,000180,000220,000308,000SingaporeYes (One)Marriott, Amex, Chase, and Citi
Singapore Airlines (NYC)120,000190,000236,000304,000SingaporeYes (One)Marriott, Amex, Chase, and Citi
British Airways 100,000200,000300,000400,000American or JALNoMarriott, Amex, Chase
Delta90,000N/A350,000N/ADeltaNoAmerican Express and Marriott

Alaska Airlines Mileage Plan (you can book on the below airlines. Points are for one-way travel)

  • American– Economy (40,000), Business (80,000), and First (110,000)
  • Cathay Pacific- Economy (40,000), Premium Economy (47,500), Business (60,000), and  First (80,000)
  • Emirates- Economy (65,000), Business (120,000), and First (225,000)
  • Fiji Airways- Economy (40,000) and Business (55,000)
  • Korean Air- Economy (85,000) and Business (125,000)
  • Qantas- Economy (42,500), Premium Economy (47,500), Business (55,000) and First (70,000)

Virgin Atlantic (Points are for roundtrip awards. One-ways for half price)

  • Air New Zealand– (60,000 points in economy and 90,000 points roundtrip in Business from LAX; 80,000 points in economy and 125,000 points roundtrip in Business from SFO/IAH/YVR)
  • Delta– Economy (100,000) and Business (150,000)
  • Virgin Australia– Economy (94,000), Premium Economy (141,000), and Business (188,000)

Direct Flight to Auckland

  • Honolulu: Hawaiian and Air New Zealand
  • Houston: Air New Zealand
  • Los Angeles: Air New Zealand and American
  • San Francisco: Air New Zealand and United
  • Vancouver: Air New Zealand

Direct Flights to Sydney

  • Dallas: Qantas
  • Honolulu: Hawaiian, Jetstar, and Qantas
  • Houston: United
  • Los Angeles: America, Delta, Qantas, United, and Virgin Australia
  • San Francisco: Qantas and United
  • Vancouver: Air Canada and Qantas

Direct Flights to Brisbane

  • Honolulu: Hawaiian
  • Los Angeles: Qantas and Virgin Australia
  • Vancouver: Air Canada

Direct Flights to Melbourne

  • Honolulu: Jetstar
  • Los Angeles: Qantas, United, and Virgin Australia
  • Vancouver: Air Canada

Other Routings to Sydney- Cathay Pacific via Hong Kong (one of my favorites); China Southern via Guangzhou; Fiji via Nadi (great if you could do a stopover); Xiamen (China, but long layovers and inconvenient routings); China Airlines via Taipei; Singapore Airlines via Singapore; Air New Zealand via Auckland; Japan Airlines or ANA via Tokyo; Korean or Asiana via Seoul; and Philippine Airlines via Manila. 

Other Routings to Auckland- Korean Airlines via Seoul; China Eastern via Shanghai; Air China via Bejing; Cathay Pacific via Hong Kong; China Southern via Guangzhou; Phillipine Airlines via Manila; Thai via Bangkok; Singapore Airlines via Singapore; Qantas via Sydney/Melbourne/Brisbane/Cairns/Perth/ Adelaide; LATAM via Santiago; Fiji via Nadi; Air Tahiti Nui via Papeete; and Virgin Australia via Sydney.