Jeff,
When you mentioned the Vatican, I presumed you would also visit Saint Peter's Basilica. So I sort of left it out in my above suggestions.
I will give you my take on my visits.
Hands down, for me, that is my most favorite and most memorable basilica. I visited Saint Peter's a number of times and was so enamored by it.
I had a couple of special experiences there which are reasons I hold St. Peters near and dear to me besides it being a breathtaking beautiful Basilica.
The Piazza is very welcoming.
Looking up at the saints statues, they have this command of gentle protection. I visited Rome twice so far in the month of December.
The Nativity was carved from sand imported from Venezia, making it extra special. The carvings were so lifelike. The special Christmas tree sparkled beautifully and added to the ambiance.
Going to St. Peters at different times of the day will give you different experiences - morning, afternoon, evening.
The inside of the Basilica, when you first walk in is just breathtaking, awe-inspiring and amazing!
To your right will be La Pieta; it does invoke emotion in some people. It is a gorgeous piece of art. Can't stop looking at it (for all it's meaning.)
Farther down, also on your right, will be the chapel of the Blessed Sacrament. Gorgeous too.
It is a chapel for reflection, prayer and silence only - no photos or talking is well enforced. Guards are there.
There are many beautiful altars and statues in the the Basilica; of course the most popular St. Peter. There are altars in the church with pews where you can sit, rest and reflect.
There is a lot to see in the basilica if you are inclined. Also, if you want, you can collect a little bit of Holy Water. You can bring your own little bottle or buy one at the gift shop.
https://www.tripadvisor.com/LocationPhotoDirectLink-g187791-d7086317-i112611309-See_Rome_With_Me-Rome_Lazio.html
http://www.vatican.va/various/basiliche/san_pietro/index_it.htm
It does have the tab to translate into English.
The basilica is free to enter whether you do a self visit or go in after leaving The Sistine Chapel after a tour of the Vatican.
There is a bag security check. No big or extra large backpacks or bags, no umbrellas. No food but bottled water was accepted as long as it was put in your bag. Bags of about 14 or 15 inches (or smaller) were okayed by the security guards. Mobility devices were allowed as well.
Like the Vatican, St. Peter's Basilica has the same dress code.
I could write on and on about St. Peter's Basilica because I love it so much. Each person's visit will be individual of course.
Behind the Basilica, you could walk into the Borgo Pio area - five minutes. A little different World leading to other areas.
There are many little shops and restaurants around.
I gave you the basics, and if you visit, I hope you really like it.
