What is that "magical" time of day to look for the cheapest and best airfare rates online?

Not true. Generally airfares are adjusted about 3 times a day as conditions change, but these changes are usually minor UNLESS there are promotions. Mostly the market drives the prices up and down. Kayak.com is one of the best comparison tools because it includes Orbitz fares as well as many others. Try to use a flexible "window" of time during which you can make the trip to get the best rates. Generally and ironically the fare from the actual Airline will be more than from consolidators like Cheaptickets, Orbitz, or others.