Today I met with a couple of other mums and their girlies for lunch at the Wild Jordan Nature Centre. It is located after the 1st circle, above the old city of Amman and with fantastic views over the Citadel as well as the famous flag of Jordan (which is absolutely huge!). You can see it on the left hand side of the picture below.
Then you have the restaurant located on 2 floors (one smoking, one non) as well as an outside terrasse I think, but it didn't look open and don't know if it was easy accessible with a stroller.
All in all a nice and refreshing place to come and enjoy some amazing views, and contribute as well to the protection of Jordan's fabulous nature heritage.