Turin, Genoa, Pisa, Florence, Volterra, Siena, Rome, Naples (This is for two weeks)
If you're spending time in Rome and you're interested in museums, then my absolute favourite is the Capitoline Museum, which you'll find on the Capitoline Hill, around the back of the
Altare della Patria (which you'll have a hard time missing as it's a giant faux-Roman building behind the Roman Forums).
On your way around (if you're looking at the front of the monument you want to be walking down it's right) you'll pass by the last remaining Roman Insula in Rome, which was the ancient roman paupers apartment (very few other equally preserved examples exist. Most are the ones that were excavated in Pompeii).
Just a short distance from that and you'll come to some massive marble stairs with two giant statues on top, and beyond that is the Capitoline Museum.
It has hundreds of Roman statues, as well as numerous gravestones and the like. It also has part of the original foundations of the Temple of Apollo, sections of a Collosus of Constantine, the Collosal statue of Marcus Aurelius, and
The Dying Gaul (which I think is a really beautiful sculpture).
Furthermore there's an opening on the second floor of one of the buildings (can't recall which, but it's the one with the funeral stones), that gives you a stunning view of the Roman Forum. It is well worth seeing, particularly if you get into the museum towards closing time at dusk. But definitely give yourself ample time to look around the museum, as it has a massive collection to see.
Also make sure you visit the Roman Forums, as they're well worth seeing. Entry to that also gets you entry to the Palatine Hill, which was the most prestigious hill in Rome where senators and Emperors lived. Today it still contains the house of Augustus (the first emperor) and his wife's house.
The Palatine Hill also leads you out onto the Colosseum, also worth a visit.
And prior to entry to the Roman Forum are the 4 other forums, Caesar's Forum, Forum Augustus, Forum Nirva and Trajan's Forum, which you can look over and into. Trajan's Forum contains Trajan's Column, which you'll spot from a distance away.
At the end of Via national socialistonale, which is the large street leading from the Termini train station out towards the forums, you'll find the Imperial Forum Museum, which has a large number of brilliant statues and pieces from all the forums.
It also lets you get into Trajan's Market, which you can see from Trajan's Forum.
It gives a really great view of the forum complex.