We also did a day trip to Rome but it’s not the best place to start from. Three to four hours on a coach, max three hours in Rome, then another 3-4 hours on coach back. A bit like staying in Leeds and taking a day trip to London
Good idea, but it’s only an hour on the fast train (Frecciarossa). Trenitalia web site says 1 adult + 1 child on 16/10 Naples – Rome = 30 Euro leave 9AM, arrive 10:10
Take an evening wander up Spaccanapoli/via dei Tribunali stopping for pizza at di Matteo or Gino Sorbillo. di Matteo is very cheap, basic and excellent. Sorbillo, less cheap, less basic, as good/better
Also, allow half a day at least for the archeological museum. A lot stuff from Pompeii/Herculaneumis on display there.