Rome is one my most favorite cities in Europe. The history and ancient buildings are what make it so special. Aside from the culture, the pizza, gelato and shopping, etc. make it such a great city to visit, 

Things to do: 

walk up palatine hill

colosseum 

trevi fountain 

tour/visit vatican city

pantheon

spanish steps

walk across the bridge to trastevere 

Restaurants: 

Emma pizzeria (pigna) ☆ 

Fortunato (near pantheon)

Fiocco di neve (gluten free gelateria, vegan options)

Clemente alla Maddalena

Obica mozzarella bar

Dar poeta (great spot for lunch in trastevere)

Shopping:

LOL boutique (monti)

Delfina (ponte)

Via condotti (main shopping street)