Based on my own experiences as an American in Israel, I would say that while most Israelis do speak English to a certain extent, it is still useful to be able to read Hebrew and know some key phrases, like “How much?” and “Where is the bathroom?” If your kids have taken any sort of Hebrew class, they probably know how to read. If they don’t know the useful phrases already, they could probably learn them with minimal coaching. If you have 11 months, you may as well try to learn some too. Even though Hebrew is quite different structurally from English, it is a lot more regular. Spelling is almost entirely phonetic.
When it comes to sight-seeing, what you should see depends on what you’re interested in. I’ll try to categorize:
Museums: First, Israel Museum in Jerusalem (including the Shrine of the Book, where they keep the Dead Sea Scrolls.) There’s a great museum in Tel Aviv called the Eretz Israel Museum, not to be confused with the Israel Museum in Jerusalem. The Eretz Israel Museum has some great exhibits about Middle Eastern crafts, Israeli history, and archaeological excavations. There’s Yad Vashem, the Holocaust memorial museum. That is always a sobering trip to make, especially with children, but if they have any relatives who were Holocaust survivors/escapees/victims, it can be quite meaningful.
Nature: The two best places to hike are probably the Golan Heights and the Negev area around Eilat. The two places are completely different, but both beautiful. Make sure you go with an experienced guide, and make sure the guide has a map. While many trails are marked, it can still get confusing. As has been previously mentioned, the Golan heights has some left-over mine fields and you really don’t want to stumble into one by mistake. If you are into interesting geological formations, take a trip to Makhtesh Ramon. A good spot for kids is the Biblical Zoo, which has more than just biblical animals. If you like biking, there’s a trail you can take that completely surrounds the Sea of Galilee. There are also some boating/rafting places on the Jordan River, but depending on the time of year, the water may be really low. A good place for a beautiful nature walk with opportunities to dip your feet in water is Ein Gedi.
If you spend any amount of time outside, drink plenty of water and wear the strongest sunscreen you can find. The sun will be a lot stronger than you’re used to, and you really don’t want to get dehydrated on the side of a mountain, trust me.
beaches: I’ve been to Tel Aviv, Netanya, Herzeliya, Eilat and the Dead Sea. My favorite was by far Herzeliya, but it’s really hard to get to by public transportation. I was going there from Jerusalem, and it took 3 buses and about 3 hours each way. If you happen to be in Tel Aviv it’s much easier. You could just go to the beach in Tel Aviv, but at least the spot I was at wasn’t the greatest. My second favorite was Netanya. They also have a place where you can go horseback riding. The area around the bus station is kind of seedy, but the beach is nice. Eilat is great in some places and really seedy in others. You pretty much get what you pay for. Still, the beaches are nice and you’re near some great hiking spots. I remember one spot on a hike where we could see 4 countries: Israel, Egypt, Saudi Arabia and Jordan. I personally hate the Dead Sea, but even I think it would be a shame to not see it even once. It’s salty, slimy and smelly, but there’s nothing else like it in the world, and it is pretty cool how you float in the water because it’s so salty.
In Jerusalem, you MUST visit the Old City. Make sure you get to the Western Wall, and try and get a tour of the Southern Wall Excavations. If you really like Biblical history, take a tour of the City of David as well. I think the second most interesting place for Americans is actually Machane Yehuda- the open-air market. Its busiest time is Friday afternoons, so you probably do not want to go then. It gets incredibly crowded and overwhelming. Another major tourist spot is the pedestrian mall based around Ben Yehuda street. This book of walking tours is pretty good.
An often-overlooked town is Safed, the home of Jewish mysticism. Pretty, interesting, historical town. Be prepared for climbing up and down lots of stairs as it’s built in the side of a mountain. It has a well-known artists colony in the summer. Near the Sea of Galilee.
For beauty and history, go to Akko and Caesarea. I can’t say much cuz I’ve never been to either, but I’ve never heard anyone say their trip there was a waste of time.
If you’re there at the right time and have strong stomachs, you might want to attend the Samaritan Passover celebration.
Masada: Interesting if you like that period of history. If you decide to do the climb up the mountain make sure you start really early in the morning so you avoid the worst heat. If you don’t want to you can take the cable-car up.
This is just a brief summary of things to do in Israel. I certainly left many things out and didn’t do justice to the things I did mention. If you have any questions about what I put down here feel free to PM me!