I was in Israel two years ago. Also spent a few days in the southern West Bank. Really the West Bank has been essentially carved into two halves. Just look at a map. The lack of contact between Israelis and Palestinians was surprising and perpetuates mistrust and misunderstanding. Things were much more separate than I expected. Palestinians were very welcoming, in need of tourist spending but also wanting to get their story out to the world. Just normal people going about their daily life, while subject to various hassles and humiliations.
In Israel proper, I thought Jerusalem was amazing. And for anyone who goes, the Tel Aviv airport is 20 mins from Tel Aviv but only 35 mins form Jerusalem, so go to Jerusalem first. TA had nice cafes and restaurants, but was pricier and not that interesting for us. It's supposed to be quite fun during the Summer, but we were there in Feb. Nazareth and the North was interesting as well. Nazareth the main Arab-Israeli city and known for its food scene.
Actually planning a possible trip to Lebanon and Cyprus. And considering flying into Israel and spending a few days to do things we missed (Masada, the Dead Sea for more than the 15 minutes we had there, the Jordan River baptismal site, maybe somewhere in north West Bank such as Ramallah).
Unfortunately, you can't cross the IL/Lebanon border.
While Lebanon doesn't allow anyone who has been to Israel to enter Lebanon. I have a new passport so my Jordan exit stamp can't be found. But my travel mates could be found out. Tricky.