For just two days, I would suggest fewer ticketed sites and more time walking around and soaking it all in. When we were there in November, one of my friends was fixated on Carciofi alla Giudia [deep fried artichokes "Jewish style"] and she was told that the REAL artichokes wouldn't be in season until January. So perfect timing for you. You could combine a walk through the Jewish Ghetto with a pursuit of one of the signature dishes of Rome. You could use the walk in the Rick Steves Rome guidebook as a template, but I would extend it to walk through the ruins behind the Teatro Di Marcello, which is similar to what you would experience at the Forum, albeit on a much smaller scale.
From there it's an easy walk to the Victor Emmanuel monument. To the right of it is the Michelangelo Grand Staircase, which will take you up to the Piazza del Campidoglio. If you head to the rear, between the buildings that comprise the Capitoline Museums, you'll find two overlooks with great views of the Roman Forum - no ticket required.
Those views, along with a stroll down Via Del Fori Imperiali past the Imperial Forums toward the Colosseum, may give you enough of a view of ruins so that you wouldn't need to spend more time going inside the Forum and Palatine Hill.
Another easy view of ruins is at Largo Argentina - while the ruins can be viewed from the sidewalk, it's now open as a tourist site, when you can buy an inexpensive ticket and descend to the level of what's left of the ancient temples.
As others have suggested, the Borghese Gallery is an efficient way to see great art without crowds - timed entry ticket must be bought well in advance. The better-known churches are another option - great art and architecture available just by sticking your head in the door as you walk past.
