Rome--7 days with wife and 10 yr old daughter who loves walking.
Rome is "the" city for that. I always like to say, "Rome in itself is a walking museum." Almost every attraction is within a 10-15 minutes walk of each other. It's always good to look at a map of the city centre & plan in "real time" - geographically - the distance or closeness. Of course this is so you're not backtracking or going in circles. (A rookie mistake, lol)
"If" you ever want or need to take a bus or metro, BIT are sold at Tabacchi shops (T), mini markets, a lot of gift shops. A single ticket is 1,50€ - after validation, good for 100 minutes of ride including a transfer. The metro is the same price but after validation, is for one ride only.
If you're going to the Vatican City, it's walkable; a decent morning walk. Go very early especially in the "now" peak season.
I always like to suggest watching https://www.skylinewebcams.com/en/webcam/italia/lazio.html
The cams are strategically placed so you can get a bird's eye view of each Piazza and/or attraction.
Read each attraction's policies regarding bags, etc. Changes have been made to some regarding schedules, policies, etc.
*The Borghese Gallery does not allow any bags - even a mini purse. Need to check them. I would not. It may be 'ok' to wear a money belt concealed under your clothes to secure money, cards, PP, etc.
*The Vatican & St. Peter's (most of the Churches), require women & men to cover their shoulders & knees - no sleeveless tops, no revealing tops, no shorts above the knees. There are no exceptions with the guards. Your wife & daughter can bring a light Pashmina or similar to cover shoulders or wear as a skirt.
They will allow small to medium sized bags (totes, purses, backpacks) - around 14" is safe. The bags are put on the belt to be scanned. Water bottles (no food) were allowed but had to be put into the person's own bag.
If the bags are too stuffed or deemed too big by the guards, you'll need to check them. You want to avoid this - because, if you're going to St. Peter's directly after The Vatican/Sistine Chapel tours, going back to retrieve your bag(s) will impede your visit to St. Peter's. You would then have to retrieve your bag(s), go back out & around to the security line at St. Peter's.
When in The Vatican or on a guided tour, you are simply led out of The Sistine & left off at the terrace entrance to St. Peter's Basilica. No security check at that point.
On its own, St. Peter's Basilica is free to enter after a security check by the guards.
*The Pantheon is an active Church so policies apply. The Piazza della Rotonda is beautiful & lively.
For some tips & fun viewing, I always suggest to peeps, The Roman Guy - They give good tips, some valuable information, and they are fun to watch. Scroll through some of their videos of Rome's attractions & its neighborhoods to help plan your 7-day trip.
https://www.youtube.com/user/TheRomanGuyTours
For The Colosseo - https://www.coopculture.it/en/it/colosseo-e-shop.cfm
For The Vaticano - Scroll through to see what meets your interests http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/visitatori-singoli.html#lnav_explore
For The Borghese - http://galleriaborghese.beniculturali.it/en/visita/visit-the-galleria-borghese
For the above three, tickets can be very hard to secure. Sometimes, if you book a tour (make sure it's an official one), you can get a valuable history & arts lesson. You do not need to buy "skip the lines tickets" some rogue vendors may be selling. They won't really help you get in faster.
If you want to invest in a guided tour, check out The Romany Guy, Walks of Italy, Dark Rome, and Eternity Tours.
The Roman Guy & Walks of Italy get very good reviews. I think they offer a discount for multiple bookings.