If you want a cheap flight from Birmingham USA to Tokyo, you've got zero airlines to choose from.
New Tokyo International Airport is just one of the airports in Tokyo. If you're not set on a specific airport, try changing your search from New Tokyo International Airport to Tokyo to see a broader range of flights – they might be cheaper.
You can expect accommodation prices to be higher at this time of year too. Last-minute deals do crop up, but it's best to book everything in advance to avoid disappointment.