Must visit:  

  • Villa Borghese , 10 minutes walking from metro Flaminio-Piazza de Popolo station.  Worth the walk. 
  • Piazza de Spagna, Spagna metro station.  Worth going at night since lots of people gather around the steps and sing.  
  • Colosseo, Colosseo metro station, or maybe better go with hop on-hop off busses.  It drops you there and picks you up from the very same location.  Take a lot of pictures.  The remains of the building are an art.  Roma Pass will let you bypass the line and get in without paying. 
  • Piazza del Popolo, again you can go with the same hop on-hop off bus and take a walk to via del Corso where you can buy jeans.
  • Vatican city, many metro stations to go there.  As the line for tickets is big, the best thing you can do is to book your timed tickets in advance from their site,  These tickets allow you to bypass the line at the appropriate time.  No waiting.  
  • Castel Sant' Angelo, near the Vatican and just across the Tiber river.  There are spectacular views from the Castel and you can drink a glass of wine on the last floor in a beautiful small cafe.  About the tickets, it is not expensive but you can buy a Roma pass and can go for free, just show your pass and get in.
  • Fontana di Trevi, metro station Barberini, you'll have to walk a little, but since you are in a new city you won't mind.  You'll see plenty of fountains in Rome, but fontana di trevi is the one you shouldn't miss.  Arrived at the fountain around 21:00 and had ice cream from a small shop across, many flavors you'll have the chance to taste there.  Make a wish and throw a coin in the fountain.
Must do:
  • All the above, when you visit all you want to visit is doing exactly what you should have. 
  • Take the hop on-hop off bus, it will take you everywhere, from early morning to late afternoon.
  • Buy a souvenir.
  • Throw a coin to fontana di trevi.
  • Eat ice-cream across Piazza Navona.The Tre Scalini on Piazza Navona is the place to eat the famous Tartufo dessert, a rich handmade chocolate ice cream roll. It's worth if you take your time eating and enjoy taking in the scene. So just think of it as the price for some great outdoor entertainment. You can also get the tartufo to go if you prefer, for half the price.
Must eat/drink:
  • Pizza, the most famous Italian pizza with mozzarella and tomato-ate it will be delightful at Pizza Re.Via di Ripetta 14. Had the best Calzone have ever had. It´s a simple pizzeria that serves delicious pizzas for a very reasonable price. The service is friendly and fast.
  • Sandwich traditionally with mozzarella and tomato, it's tasty and big and it will keep you full.  Cheap & chic. Il Delfino
    Corso V. Emmanuele 67. Extremely friendly and kind people.
  • For a cheap place you can try Sfizio Pizza. Delicious big pizza but also other Roman specialities. Clean and fast. Via Giolitti 77

Hope someone finds this helpful and have a nice trip.  Rome is beautiful and as expected most beautiful thinks are free.