Jordan is the safest place in the Middle East, we should walk around and you will say so and it is a fact.
You can enjoy travelling all over Jordan day and night and you will feel have safe as a fact.
Petra, the other name of the Jordan, as soon as you says Jordan you mean Petra.... and as soon as you say Petra you mean Jordan...
Aqaba, Jarash, Ajlon, Wadi Rum, Um Qais other places you should visit...
What more, you have Amman, the nice capital city, you will enjoy going to some nice places there.. Abdoon, Sowifya, and some times will enjoy Shimissani