Wow, I need a book to respond. There is the Negev in the South and in the North you have places like Cesearia, Akko, sites in the Galilee and the Golan. Depending upon your religion you may want to go to Bethlehem or Hebron. How much you explore and what should be a priority depends upon the time you are spending in Israel. Within each city there are places that are better seen with a guide and then there are others that provide audio guides or guides that can be downloaded to smart phones.

This is a link to a non-commercial travel guide to Israel that contains many excellent suggestions:
http://amateurtraveler.com/travel-gu...el%20guide.pdf

Other links:
- Gov't tourism web site: http://www.goisrael.com
- Tel-Aviv tourism: http://visit-tlv.com/
- National Parks http://www.parks.org.il/parks/ParksA...ranceFees.aspx
- Museums: http://ilmuseums.com/
- "Time-Out Magazine: http://digital.timeout.co.il/english/

I would leave Jerusalem for the last part of the trip (but at least 4 days). It's a good choice to begin discovering Jerusalem with a tour (for the first day) and then continuning on your own.
Also - don't miss the Dead Sea - the lowest point of earth and a natural wonder - you float. And the nearby Masada National park.

Jerusalem official tourism website: http://www.itraveljerusalem.com/
Haifa official tourism website: http://www.tour-haifa.co.il/eng/
The Dead Sea ( http://www.deadsea.co.il/en )
The old city of Akko ( http://www.akko.org.il/en/ )