Some of the sites I'd really recommend are Nazareth basilica, Masada, Jafa, the citadel and the turkish bath of Acre, the centre of Jerusalem, the diaspora museum in Tel Aviv's university campus, Apollonia national park and Caesarea Maritima national park. If you want a taste of israeli culture, amongst others, these are the places to go. Once you've had enough of history, you could also go to one of Jerusalems zoos or to the souks (markets) that you can find in most towns.
Israel is also ideal if you're a shopper or a party goer. Tel Aviv is considered one of the cities that never sleeps. It also has some huge shopping centres, open all week a part from saturdays (there are a few exceptions).
It's also a must for divers. It has some of the best diving schools and the sea is warm, especially in summer, which is always a plus.
If you like food, you can most certainly find what you're looking for. Due to all the different nationalities you can find in Israel, there are quite a few different restaurants. You can find italian, european, modern and american food, meat bars, fish restaurants and of course the local mediterranean and middle eastern gastronomy.