We mostly fly United out of Newark, and I've found that there is no certain day of the week when the prices are lowest. On our last trip, the Sunday price was the best - much lower than the following day. If your scheduling is flexible, go to the airline's site and research the basic time period when you want to go. On United, you can do a calendar search for the entire year (for the dates that they've released) and see how widely the fares vary. After we've found airfare, then we decide on accommodations.