There was a Kosher restaurant in Amman, Jordan but it closed. I was in Jordan, but it was a day trip from Eliat to Petra. Petra was really cool.
Lebanon you need to be careful of, you are not allowed to enter Lebanon with any marking of having visited Israel nor are you allowed to bring in anything with Hebrew Language on it.
When you cross the border from Israel to Jordan, the Israelis might not mark your Passport, but the Jordanians do and if the Lebanese see Arava Crossing for example in your passport they will not let you in.