As a US citizen with a US passport with an Israeli stamp in it you should have no issue entering (assuming you have appropriate visas is applicable):
Thailand
Singapore
Hong Kong
China
South Korea
Japan
Australia
Fiji
New Zealand
Cook Islands
Anywhere in the EU (including but not limited to:Italy, Germany, Netherlands, France, Spain, Switzerland, U.K, Ireland, Iceland, Poland, Czech Republic, Greece, Sweden, Demark)
I can't answer for the other countries.
Sounds like an awesome trip!