Lovely, what hotel are you at?
Theres an absolutely amazing Bakery/Deli just down the road from the collesseum. Its off a side street just on the opposite side to the collesseum entrance.
I would make a list of the things you want to see and plan it on a map, the only thing i think we missed out on were the catacombs.
We just walked from the Station to our hotel which was quite close to yours. Its probably only about a 15/20 minute walk. Otherwise there is a metro station quite close.
Trams are a good way to get around, although we just wandered around a lot and came to places as we came accross them.
One day that we enjoyed was to get a tram up to the Vatican, have a walk around the vatican area (i wouldn't pay for a tour) Definately walk up to the top though, the views are excellent.
From there you can walk down the river through the Trastevre (i think) area and it takes you right down to the collesseum.
Bit like this
The deli i mentioned is on one of the crossroads just under the Via Labicana to the right of the collesseum.