One thing immediately apparent in Rome is that you will stand out as a tourist and will be surrounded by street sellers hawking tours, phone chargers, selfie sticks and umbrellas if it rains. My advice Is to not buy any tours and do it yourself, get a map beforehand and plan what you want to see. Work in the tube stations so that you have an escape route when tired. If your phone allows it use your navigation between sites, it is great to know how far away you are from your target.
What to visit? Of course go and see the Vatican and the Colosseum. Our high was the Pantheon one of the oldest buildings in Rome and must be one the most magnificent. Our low point was the Spanish Steps, rechecking our location to make sure we were in the right place. We did not go inside the Vatican as the queues were very long even in the pouring rain. Instead we visited the basilica Santa Maria Maggiore where there is no entry fee, but you will not be disappointed it is a spectacular building. The Colosseum is undergoing repairs but it impressive none the less and like the Vatican has long queues. Also under extensive renovation is the Trevi fountain with statues and carvings being replaced.
Food in Rome like most of Italy is excellent and mostly good value but like anywhere excercise caution and check menus first, good places are not hard to find. For lunch check out the Dakota burger restaurant between the Pantheon and the Trevi
Overall we enjoyed our visit but like a lot of major cities suffers from decay and basic untidiness but unfortunately in Rome this includes around all the major historic sites.