There's no "best day" to book a flight. General consensus in the travel industry is that you should book domestic flights about three months out. I check with Google Flights to see if the current fare is above or below average and decide accordingly; they offer a fare watch service that you can use if you want to gamble (with their data to back you up) that the fares will drop.
Southwest is an exception, but even they don't always post their lowest fares when they're published, as they have sales often and oftentimes the prices drop. Sure, you can rebook and get the travel credit back from them, but then you're having to keep track of the travel credit. If you use SW miles, they'll just credit you the difference in the form of miles credited back to your account, no strings attached.