Specifically, plane tickets usually don't get cheaper closer to the departure date. Instead, flights tend to be the most inexpensive when you book between four months and three weeks before your departure date.
What days of the week do flights drop?
The cheapest days to depart if you're flying within the U.S. are midweek — generally Tuesday or Wednesday. For economy tickets, Tuesdays are about 24% lower than peak prices on Sundays, which translates to savings of about $85 per ticket. The same is generally true for business class and first class travelers.