Never been to Naples so can't advise you there.
Best tip for Rome - take comfortable walking shoes. You will walk and walk, it's the easiest way to see the city.
Plan to see the main sights, but also leave time to just wander, you will come across beautiful sights just wandering the side streets.
Take a small drinks bottle and fill it up at the water fountains all over the city.
If you like wine, visit Cul-de-Sac, just off the Piazza Navona, for a huge selection, ranging from reasonably priced to very expensive. Full of locals and very busy, so be prepared to queue a bit.
If you have time, visit the Piazza of the Knights of Malta, and look through the keyhole of the gate, it will make you gasp!
Most important of all, throw a coin in the Trevi Fountain, to ensure you will return to Rome, it's the most amazing place.