Here are two Roman museums I really recommend.
Museo di Roma in Trastevere
This museums shows the history of Rome from the 18th century untill now, focussing on festivals, streetlife etc. Due to restaurations I could only visit the second floor, but here I saw a beautiful exhibition of watercolours (1900) from places in Rome, and one with photographs from Rome, dating from the end of the 19th century.
In this large palazzo once owned by the Barbarini family there is now a museum, full with the Barberini's magnificent art collection.
Religious art, Dutch masters, Caravaggio and his followers, portraits of Erasmus and Beatrice Cenci.
Every time I visit I wonder which paintings will be on display, since not all rooms can be visited all the time due to maintenance.
The palazzo itself is also beautiful.