St. Peter's Basilica, Vatican Museums & the Scavi Tour
Living in Italy and being a Catholic is an amazing thing. Getting to be up close and personal with the home of my faith has truly been a wonderful experience. I feel beyond blessed to have been able to not only see the Pope three times, but also to have had the opportunity tour the Vatican multiple times has inspired me to pinch myself to make sure I wasn't dreaming.
St. Peter's Basilica at night, is empty for the most part of the hustle and bustle of the day time. It's quite lovely and peaceful. 
Standing outside of Vatican City (i.e. in Rome) it is impossible to not be approached by one of the tour guide services. I've done the tour guide thing, and it was great, but depending on which tour you purchase they can be pricey, and often you miss a lot. It's practically impossible to see all the incredible art the Vatican has, most tours and tourists go to see only the most famous pieces of art think Raphael and Laocoön,...
However the Vatican has so much to offer, that in a smaller museum would be the reason why you'd visit. I'm talking Salvador Dali, Rodin, and even Van Gogh. This painting is his Pietà. 
Yes. The Vatican is full with art from the Egyptian era to our current time, but spying one of Rodin's "The Thinker" pieces took be straight back to my high school World Literature class where we learned about this sculpture and his famous thinking man.If you'd like to or are able to dedicate a full day or at least half a day to touring the museum you can certainly do so with out the aid of a tour guide. The museum offers a map and audio tour guide thing-a-ma-bobs for a small fee, you can plug into your ears and learn yourself. I will say the benefit of a tour guide is a lot of the behind the scenes history of the pieces etc., which I did enjoy when I toured the the museum the first time with a guide.
Here my son Michael and I are pictured in the Hall of Maps.Another perk of having a tour guide is that you can enter St. Peter's Basilica without having to go out and make the line to get in. This you do after the Sistine Chapel. I may know of a certain family, short on time who followed a group with a tour guide out and made their way into the Sistine Chapel with no problems... this is however, against the rules...
Upon entering the Sistine Chapel, one of the first pieces of art you will encounter is Michelangelo's Pietà. You can also pay to have a tour guide show you around the Sistine Chapel, however I strongly encourage you to contact the Pontifical North American College in Rome, to schedule a tour with one of their seminarians. American seminarians are available for free tours of St. Peter's Basilica on Monday, Tuesday, Thursday, & Friday at 2:15. The tours are free, but since they don't really earn any money while studying it's nice gesture to offer them a tip.
Another lesser known tour available is the Scavi tour. This tour will take you to the excavations of the necropolis beneath Saint Peter’s Basilica and the burial place of Saint Peter himself. I had an amazing experience when I went on this tour. The Vatican only allows only a very limited number of people on this tour per day, and the minimum age is 15 years. If you wish to go on this tour, make reservations a few months ahead of your trip. You have to request tickets from the Scavi tour office itself. Information to do so can be found on the Scavi and Catacombs information page of the Pontifical North American College.Do you wish to see the Pope? For information on how to get your tickets for a papal audience or Mass, please check out this post: How to get tickets to a Papal Audience and Tips for Getting the Best Seat
Trevi Fountain at Night and Visitor Tips
The Trevi fountain is a gorgeous beast. It's Baroque style is breathtaking, I dare say there is no other fountain more gorgeous, it is even more beautiful at night. The Trevi fountain is open 24/7 and it is absolutely free. You can sit and gaze at it for as long as you wish, though it's usually most crowded from around mid morning through the evening hours. The best time to view the fountain if you'd like to have it more to yourself is either after Midnight or in the very early morning hours. There are lots of vendors selling stuff, guys handing you roses (they're not free so just say, "No grazie", unless you wish to purchase one.) and photographers selling photos. As with any heavily populated tourist ridden area in any city in the world, be sure to guard your belongings and be smart. Have your coins ready to be tossed before you get to the fountain to avoid having to dig through your wallet.
If you're a fan of the film Roman Holiday staring Audrey Hepburn and Gregory Peck or Three Coins in the Fountain,then you're familiar with the legend surrounding the fountain. I've heard of a couple of legends the first being that if you toss a coin with your back to the fountain using your right hand over your left shoulder then you will return to Rome one day. A newer legend says the first coin you toss into the fountain will ensure you're return, a second coin will mean a new romance, and the third that your romance will lead to marriage. Both legends stipulate having your back turned, and tossing the coin over your left shoulder using your right hand; however if you take a moment to watch other tourists they seem to use both hands... I'm not sure if this is an unfamiliarity with the legend, or if I'm the one who is mistaken.The best part of the coin toss is how the money is used. Nightly about €3,000, is collected and given to a local supermarket which serves the poor, and other local charities like the Italian Red Cross. 
There are lots of gelato places and restaurants around the fountain, but they can be pricey and sometimes the quality of food isn't the greatest. Be sure to check reviews if possible before making a decision to dine.The Trevi Fountain is easy to get to, if you're traveling by the metro use the Baberini stop on line A.