Italy's most visited attraction is the Vatican Museums and Sistine Chapel complex. Through October 26 you can visit them on Friday nights when they're open from 7-11 PM. Advance booking is required for the night visits but be sure to book your ticket ahead no matter when you go so you can spend your time inside the museums rather than waiting in line. Tickets can be booked from the Vatican Museum ticket office or if you're in the US you can easily book online and pay in US dollars through Select Italy (book Vatican Museums and Sistine Chapel advance tickets or night tickets).
For a really spectacular visit consider an exclusive private after-hours guided tour (booking information from Select Italy).
Notes: At the entrance you will need to show your passport to security. Be aware that you may not be admitted if you are wearing shorts, a mini-skirt, or sleeveless top.