I've been here a few times, on each occasion I did something completely different. You can see ancient excavations, biblical artifacts, ancient synagogues recreated, and Jewish art (ancient and contemporary) from around the world. My favorite is the archaeology wing here- it's quite vast and could take days to go through. I'd recommend a guided tour; a couple of them are offered every day. It can be a bit overwhelming to try and conquer even one wing on your own and the tours help to orient you in the main areas of a wing or even of the whole museum, if you take the Highlights Tour (which is great!).
I've only come here with adults, and I can imagine it may be tiresome to bring the whole family. They do have children's programs, so the kids should be entertained, although I can't vouch for the quality of the activities.
Of course, the Dead Sea Scrolls are a big crowd-pleaser and recommended as well, but don't forget about the rest of the fascinating exhibits!