Our week in Rome last week was brilliant absolutely brilliant.
Thoroughly recommend booking the colloseum in advance, it's brilliant and you wont have to queue at all.
You also get one of the forums with it too, brilliant views from the hill.
The old chariot racing area wasn't that far from there too, worth a quick wander.
Vatican museums are alright but don't expect anything except being shunted through a long museum. There's no feeling of spirituality for example, you just end up in the Sistine Chapel and although it's obviously beautiful inside, you could be fatigued with art before getting to it. I know that sounds weird but it just all feels like a rich museum rather than the heart of a 2000 year old religious establishment. The queue for the basilica was massive so didn't bother
Take the The Families Who Made Rome walking tour on guruwalk.com its totally worth it and you see most of the main spots.
Trevi fountain is alright but packed out constantly.
Pantheon is cool. Don't bother queueing on the right with the idiots, go left and book a ticket with the machines and you'll get in straight away.
Eating out, you can't go wrong but don't go with any pushy dickh3ads, plenty options.
I really liked Bascilica Di Sant Andrea della Valle. Stunning church and not tourist packed, even use it to chill for a bit.
Saint Paul's basilica to the south of th city is absolutely worth it too.
The Trastevere area is nice but getting more touristy.