I’m going to give you some non-touristy suggestions…if you have time for them. If you are history nerd, you may already know about them. By far the coolest historical site I’ve ever seen is the Necropoli (city of the dead) in Cerveteri which dates back to Etruscan times. It’s city of grass dome tombs and dirt paths they built for their dead. It’s only an hour or so outside of Rome and you can get there by train very easily. The hardest part is getting to the actual site once you arrive in Cerveteri. If you can find a bus stop…take the Blue bus and using your best Italian say you are going to the Necropoli. Better yet, take a taxi!
The second is Ostia Antica which is 20 min trip on a regional train. The ruins are fantastic and you can really imagine how Romans lived. Plus to get to that regional train you see a really cool part of Rome.
Tivoli is a good option too, only about 1 hour away by bus. You can see Villa D’Este and Villa Hadriana. Villa D’Este is easy to find (the bus drops you off right there), you can catch another bus to Villa Hadriana there too, just wait until you see an actual building to jump off. I made the mistake of jumping off too early and having to walk like 3 hours in 90 degree heat to get there.
Pompeii is great too, but staying in Naples (which is a hellhole) is not so great. But at least Naples has fantastic pizza. You can also catch ferry to Capri (I’ve never been, but I hear its lovely).
Obviously if you have limited time, stay in Rome and see it all. Pantheon, Colusseum, Vatican, Villa Borghese, Foro Romano, Trevi Fountain, Fountain of Truth, Campo Dei Fiori, Catacombs St.Agnes, Spanish Steps, Baths of Caracalla, Palatine Hill, Trajan Market (if its open again…it wasn’t 2 years ago) a gazillion cathedrals, piazzas, cappucinos and gelatos of course 🙂
How long are you there for? If you have anymore questions, let me know. I went there once for a summer abroad and then re-did the trip with my fiance 2 years ago. I still kind of remember how to get around. Another piece of advice, do not buy an advance Eurail ticket for the train. It’s a rip off. Just pay per ride like 30 min before departing, its a lot cheaper.