how are you planning to get around? I think I'd feel happy to visit the major tourist areas, perhaps flying between them, but wouldn't want to get a bus from Israel across the Sinai towards Cairo for example.
I travel regularly there for work and used to live in Jordan. It is interesting and safe. Would personally not now go to Egypt (been there in the past) but have friends who do go without issues. To be honest, there have been more attacks in London last year than in Jordan.
You may need two passports OP if you are planning and doing the three countries at the same time due to Visa issues. All beautiful countries, I preferred the desert to any were else, but if you have the opportunity then definitely go. I don't think any were is particularly safe at the moment to be honest.
You will be fine in Israel, security is very tight everywhere but it's no more dangerous than anywhere else is currently. Tel Aviv is the most amazing, fun, buzzy, modern European city. Incredible beaches, great shopping, top class restaurants, wonderful theatres and galleries and Jews and Arabs getting on with their lives and intermingling together. Jerusalem is fascinating too. It's probably a bit more tense in the old city than it is elsewhere in the city but I've never felt unsafe
Did a tour round Jordan last year and loved it. They are struggling with falling tourism because they are next to Syria so people assume it us dangerous when it is relatively safe (that said there was an attack at one of the sites we visited a few weeks later but then there have been attacks in England, France, US etc...). Stay away from the areas near Syria! Petra is amazing as are the roman ruins north of Amman. Really enjoyed floating in the dead Sea too but not that taken by Aqaba.
There are issues travelling between various countries in that area in terms of visas and having stamps in your passport from certain countries. The lonely planet guide for Jordan has a section telling you how and where to cross to not have problems.
Yes this is what I’m wondering re passport stamps and going to all three countries - can anyone advise? Unfortunately only have the one passport. Also looking at going to Russia a month before, hoping this won’t pose problems?