Do you have any suggestions for a day trip from it will be in January
what mode of transportation?
Public transportation...no car
Hands down, Orvieto was one our favorite stops. It was a nice train ride to a magical place. You won't be disappointed.
Take a look at Ostia Antica too. It's sort of a Pompeii but much closer.
Orvieto is a nice break from Rome, small hill town in Umbria, well worth a whole day, but vasically leave early morning, back in time for a late afternoon drink on a piazza in Rome.
Ostica Antica is certainly well worth the visit, but really, it is more a sight in Rome (it only takes a standard metro ticket to get there) though you should devote a half day to it.
A bit further afield would be Anzio, and with fast trains, Naples and Pompeii are not too far.
Another vote for Orvieto! We loved Orvieto; it's an easy 60-90 minute train ride from Rome and is a very interesting town. We really enjoyed the underground tour and I loved seeing the facade of the Duomo illuminated by the mid-day sun (absolutely beautiful). There's also a tower you can ascend for wonderful views. You can also visit St. Patrick's Well (we didn't have time for this) but it looked interesting as well. Have a wonderful trip!