I've been to Rome so many times because of different reasons, military, personal, business.
Here's what I gathered:
1. The Trevi Fountain was my favorite tourist spot. There is a gelato shop right beside it, it doesn't get much better than eating that gelato and staring at that fucking fountain. There is also a pub near there called the Albert. I liked it.
2. Shit/Piss before you go to see the Vatican, or you'll be shit out of luck. Insanely packed with people and no public restrooms. Not cool when you have the beer shits.
3. There is a little band that plays in front of the Pantheon at dusk at this restaurant. Do your best to eat there at dusk while they're playing. It's a great experience.
Restaurant with direct view to the Pantheon in Rome - Review of Ristorante caffe da Claudia, Rome, Italy - TripAdvisor
4. Hop a train to Florence for a day.
5. The nightlife is more of the bar scene feel. I had fun when I went as a younger guy and did all the bar crawls. The nightlife imo is so-so.
6. Try to find some Limoncello from Sorrento, not that touristy bullshit.
7. No idea if they're in town or even playing, but if so catch a AS Roma game.
8. You can walk everywhere, but it's a lot of walking.
hope this helps
