Pompeii works comfortably as a day trip from Rome. Take a high-speed train from Roma Termini to Napoli Centrale (about 70 minutes), then change to the Circumvesuviana for Pompei Scavi — roughly two and a half to three hours door to door. Leaving Rome by 8 am gives you a full day at the ruins with time to spare.
If you would rather not manage two trains and a connection, a guided day trip from Rome bundles the transport, entry and a guide into one booking, and gets you to the gate without the planning.