Israel is such a wonderful place to visit (especially because I have lots of family there, my dad lived there for many years, and my mom was born there xD). The two times I have been there I simply went with my family, but in one of the coming years I plan to go with a group (not to tour but to be active).
One group I can think of right now would be
BBYO (they have tons of places they go - look at the left side of their page where it talks about passport 2 Israel).
If you decide to go alone or with family then here are some places I recommend you visit (I won't retention the ones that were mentioned in the earlier post)
Ber Sheva -- a city (where my mom was born xD) and where Abraham built his famous well that you can actually stand over and look in
a Kibbutz -- hard to describe so
here the Dead sea -- the lowest place in the world, also the most saltiest sea in the world. In Judaism it is believed that the Dead sea is the result of when the cities of Sodom and Gomorra were turned over in The Book of Genesis
a Shul -- although there are plenty of them here, if you are not Orthodox and have never been to that type of Shul, you will be shocked when you visit a Shul in Israel. There is a whole wall down the middle only with curtains that a female can look through to see what is going on. The seats are not even the same; there are just basic tables and chars; it is a neat experience
there was also this really interesting cave I visited the last time I went but I currently can not remember what it was called. another place I would recommend simply because my grandparents live there would be Kfar Saba. (I may add more as I remember more interesting places xD)