There are so many things to do and see in Rome, that you could easily spend two weeks without getting out of the city. However, should you want to take a day trip from Rome, consider visiting Ostia-Antica. Supposing that you could only see 10 things in Rome, Ostia Antica ruins should be one of them, next to other Roman ruins in Rome and surrounding areas.
There are many good reasons why Ostia Antica is the perfect destination for a full day trip from Rome.
Rome
Ostia