My tips after visiting the Eternal City
1. Book early to find the best accommodation near the tourist sites. Since most of Rome's most interesting tourist sites are within walking distance of each other, the most stress-free way of enjoying the city is to stay close. We stayed in the neighborhood of Prati, close to Vatican City. The Vatican was only a fifteen minute walk, with the Spanish Steps, Trevi Fountain, and Pantheon, a similar distance in the opposite direction. The Colosseum and Roman Forum are a bit farther (35 minutes walking), but if you're up for the walk it's still a great location. If you would like to avoid the touristy areas, another great neighborhood is Trastevere. Trastevere is known for its quaint alleys and great food.
2. There is no Uber in Rome other than bikes and Uber Black, so you will need to take taxis, which can be quite expensive (see tip 1). Use free now if you don't feel like hailing a taxi in the traditional way. There are also taxi stands throughout the city where taxis will line up.
3. Many of the restaurants in Rome are tourist traps charging high prices for low quality fare. Use the internet to find good eating spots, and, in general, avoid eating at restaurants near tourist sites.
4. If you would like to visit the Catacombs of Rome, they are quite far from the city center, and it may be necessary to find a taxi. They are along the Appian Way and usually on private property. You cannot walk through freely, and will have to pay a small fee for a guided tour at the gate. Guided tours are usually done every hour. If the catacombs are too far you may also be interested in the Capuchin Crypt, a church with bones and skeletons arranged in interesting patterns. Beware though, it is a bit strange and certainly not for the faint of heart.
5. One of my favorite parts of Rome was the dome of St. Peter's Basilica. For 10 Euro you can walk up the stairs to the top of the dome to look down inside the church and also get a great view of Rome from the outside. If you aren't in good shape you may want to pay 2 Euro more for the elevator ticket.