Galilee is my favourite region in Israel. It is diverse but also relatively homogenous. By diverse I am talking about the rich heritage, what with Safed, a centre of Jewish mysticism; Nazareth's Church of the Annunciation; or the Druze and Circassian villages.
I really recommend going to the region during a trip to Israel. There are lots of things to see and do there. The gourmets among you can try the wine and other local specialties (cheese, olives, figs, za'atar, etc.). Those who love walking can wind along the paths of Mount Meron, the village of Rosh Pinna, or Mount Carmel. If you are passionate about history there are major archaeological sites such as Megiddo or Beit She'an.
I prefer going in the spring (which arrives at the end of February over there) because the hills of Galilee are covered in wild anemones and the almonds are in full flower.