We will be driving from Bergen County (northern NJ) to Naples Florida in a few weeks. We're planning on spending 2 nights on the road. Any recommendations? We'd prefer to have the shortest drive on day 3 so that we arrive in Naples earlier rather than later in the day.

I've driven Bergen Co to Naples quite a few times. It's about 18-20hrs total travel time, depending on traffic, # stops & speed.

If you break that into 2.5d travel, that's about 7-8hrs 1st & 2nd days, then about 4-5hrs the last day. So first night about an hour or so into NC, then the 2nd night around Jacksonville.

You can go visit Pedro at "South of the Border" which is the first exit in South Carolina.

How many miles it to "South of the Border"?

Bergen to "South of the Border" is 600 miles (9.5 hours).
Just north of Dillon SC within a mile of the NC-SC border

I go from Lambertville to Naples. Savannah is a great stop, but a pretty full day after on to Naples. It's ideal for the first night heading north from Naples, though. Next month I'll drive to Fayetteville, NC first day, then to Lake Mary (just north of Orlando) the second. Both days are about 8 hours and the last day about 4 hours.

We drive from the Phila. suburbs to West Palm Beach, FL. I know you are heading toward the other coast, but we are both heading to south Florida.
We also like to take it easy and spend two nights on the road with our last day requiring only a few hours of driving.
We usually make our first stop at Dunn, NC. The second day we usually spend the night in Palm Coast, FL. From there it's only a couple hours to our destination and we get there early enough to unpack and go food shopping.

Factor in daylight hours, rush hours, and your own body clock. I have drive Boston - NC more times than I want to remember and on to south Florida a few times.

Key is to avoid rush hours in NYC, Baltimore, DC, and Richmond (which has become surprisingly annoying with traffic). Driving southbound from Bergen County (my home before Boston) you should avoid much of NYC rush hour traffic. You don't want to leave so early that you hit Baltimore/DC at AM rush hour - but you also might not want to drive too late after dark along I95 in NC - which can be really dark and isolated.

I would leave around 6:30 AM and plan to stop somewhere right on I95 near NC/.SC border. i95exitguide.com is a useful tool. Keep in mind that in NC/SC many of the hotels are old motel-style. If you are uncomfortable with no interior corridor, verify layout.

We don't like those old motel style places and are usually able to find a Hampton Inn close to I95 for our stays.

And as you pass through the eastern NC corridor, don't forget to sample the BBQ.
As for old style, the "motels" around the Darlington exit are definitely "hotel' styles but.....
We don't use them but pass by 4 times a year on way to the beach and see them.

By the way, most direction services will aim you down I-95 to I-10 at Jacksonville, then down through "speed trap central" of Waldo, Florida to head to I-75 by Ocala, then down to Naples. I have found I much prefer staying on I-95 to I-4 at Daytona, then down past Orlando taking US 17 down to Ft. Myers and hitting I-75 there. I think Mapquest shows that as being something like 2 minutes longer, although it is conserably less distance -- but I find it much better and actually generally saves quite a bit of time as well.