For those who want to visit the Vatican Museums and the Sistine Chapel, the best neighborhood is Prati which is close to the Vatican. The area is quiet and there are numerous restaurants, cocktail lounges and wine bars at night.
Crossing the Tiber to the north you reach Piazza del Popolo, to the south are Castel Sant'Angelo and Piazza Navona.
Accommodation prices in this area can be higher but by booking in advance you can find good deals.