The only "good" time to be on that road, if there really is one!, is late at night and/or on the weekend. Even with that, Sunday is best. We used to travel from NH to NC frequently, so have had the misfortune of taking I-95 and the infamous Beltway more times than I care to remember. If you have to take it on a weekday, try to do it mid-day or late at night. Morning and late afternoon commuter traffic is an absolute nightmare. Depending on what part of NY you're in, and where in GA you're heading, you might consider I-81 in eastern PA and down through VA. We did that on our last trip to FL and dropped down onto I-77 in western VA, into NC/SC, then a quick jog on I-26 brings you back out on I-95 just above GA. When routing it on a map, we discovered it was only an extra 25 miles than taking I-95 all the way; WELL worth it to us to avoid the DC area!!
Best of luck on your trip!