Renting an apartment in Rome is a matter of choice. Usually travelers rent apartments only because they want to save money.
While this is often true, renting an apartment in Rome, in my opinion, should be a choice due to other factors, such as freedom, an immersion into the local culture, living like a citizen of Rome. The economic factor is also important however. While renting an apartment for 1 or 2 people can be not much cheaper than a hotel, when your party is bigger a rental unit makes economic sense. With a hotel you cannot cook, so your only alternative is going to a restaurant. Do this twice a day with a family of four and you end up paying a dear price. A hotel is more suited for a very short stay, while an apartment makes sense for a 4-5 night stay and up. Remember that Rome has a very large historic center and it contains about 50% of the world cultural worth; the whole country (Italy) has about 80% of all cultural patrimony of the world. I suggest a minimum stay of 1 week in the Eternal City. I lived in Rome more than 24 years and I have not yet visited all sites. My website specialized in Apartments in Rome will help you select the right accommodation for your needs. This is the link: Apartments in Rome.
Have a nice stay in my wonderful country!