I don't think any route that long could not have stress.
Basically you need to get yourself through NYC and then there are two routes I've done before. The obvious one is the New Jersey Turnpike over the Delaware Memorial Bridge and then I-95 south all the way to Daytona, then I-4 west to Lakeland. There are bypasses to consider for Baltimore, Richmond, Jacksonville and Orlando depending on rush hour. I-95 is hectic but probably the quickest.
The other route is to take I-78 west from Newark over into Pennsylvania and then pick up I-81 south from Harrisburg. This is a beautiful drive that runs down the west edge of the Appalachians to Knoxville, where you pick up I-75 the rest of the way to Tampa. (and I-4 east to Lakeland) Much less hectic and much more scenic.
I've also combined the routings by doing I-78/I-81 to Wytheville, VA and then taking I-77 to Charlotte and Columbia, SC and then I-26 to I-95 near Charleston.
But if you draw a straight line from NYC to Jacksonville you'll see that I-95 runs closest to that line.
BobK/Orlando