We plan to divide to make this trip with one or two overnight stops without making the trip longer.
Any suggestions for places worth visiting on the way?
Might you want to fly from FCO to Bari airport instead and rent a car there? Spend the night in Bari if you'll be jet-lagged.
Thanks, but we considered all options and decided to drive in 2-3 lags.
Are you going straight after a transatlantic night flight? That's going to be tiring.
I've done that drive this past month, however I was coming from up north (Tuscany), so it was an even longer drive. I passed near Rome, through the A1, however and from there I took the A24/A25 East to Pescara (which you will also take), then, once near Pescara, down the A14 and eventually to Vieste. The freeway A24/A25 (Rome-Pescara) will be one of the most memorable drives you will do. The mountain scenery (outside of the many tunnels) is gorgeous.
Coming from Tuscany it was almost 9 hour drive (plus pitstops) for me, coming from Fiumicino it is going to be close to 6 hours for you. I did it all in one shot (and it wasn't the first time I've done that stretch), but if you want to stop along the way, you might want to look into Tagliacozzo, Bugnara, even Pacentro, as possible stopovers on the mountains. However they are not exactly along the freeway, so it will be a little detour.
If you can hang on at the wheel for 3 hours from Rome, then I would consider the Trabocchi Coast of Abruzzo. Vasto or also Ortona, would be excellent choices, and those towns both are along the freeway.
From Vasto to Vieste, it's another 2.5+ hours. The last stretch just before Vieste is very curvy on mountain roads, so make sure you nice and rested before you attempt it.
What is it you want to see/do that you are planning to stretch a 300 mile drive into 2 or 3 legs?
You could stop in Campobasso and see Kelly Ripa's soccer team
https://abcnews.go.com/US/kelly-ripa-mark-consuelos-speak-david-muir-rooting/story?id=124185528
Depending on your religious bent , you may find the Padre Pio Shrine in San Giovanni Rotondo of interest.
If you take the A1 then AA85 then SS650 then onto A14 possible interesting stops are Anagni , Isernia, Termoli.
If you take the E80, then A14 possible interesting stops are Tivoli, Sulmona, Vasto, Termoli
Thanks to all for the helpful information!