SO my trip is coming up, but on the recs of my family member who is in the airlines we are doing:
NH Fori Imperiali, it is literally right next to the forum ruins, Parthenon, and lots of the main areas. It is a five star hotel.
NH is a chain in Europe. The rooftop bar over looks all of old Rome.
When we come back after touring Italy we are going to stay at the Waldorf Astoria Rome, it is more near Vatican City on 15 acres of gardens. So not close to the main parts of Rome, but I need some relax time too. They have free shuttles and fun things to do and will arrange day trips for you.
Another suggestion that was given to me:
Marriot Grand Hotel Flora, it is near the fun stuff and near the American Embassy as well.
I had the intercontinental Rome booked, but they canceled my reservation as their new big renovations will not be done till mid April. But that is where a lot of airlines put their crews.
If you want to do some touring, I highly suggest Livtours. They are a family run business, and their group size is 6! I have booked 90% of my Italy tours with them, and they have been great and communicate a lot. So far so good. The price is great for a small group.