There are few nonstop flights to Greece from the U.S., so you'll likely have to connect somewhere in

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You need to list your cities and airline preferences. Do you have status with any airline? Are your dates flexible? I use a search site Itasoftware, but you can't book with them. You can find the cheapest flights and then you must go the airline site and book. Other people sign up for fare alerts and sites such as Kayak.
Putting in some random dates in September into Kayak, car rental in honolulu hawaii it appears that flights right now are running around $900 from New York, and that is a very good fare. You will not find something car rental in honolulu hawaii under $800, so this may be a good time to buy if you are certain of your travel dates. Otherwise, start solidifying your plans and book no later than early July (5 to 7 weeks out is typically the best time to find deals). Of course, it depends on where you're flying from.
There are few nonstop flights to Greece from the U.S., so you'll likely have to connect somewhere car rental in honolulu hawaii in Europe. I believe that Delta still offers the only nonstop to Athens from JFK. Right now, it's usually cheaper to connect in Reykjavik, Oslo, or Zurich, but Lufthansa often has sales allowing you to connect in Frankfurt or (less regularly) Munich.