Amman is not the kind of place I'd go for "fun". It's a sprawling urban complex in a small and poor country. There's a Roman ampitheater in the old part of town. Good food can be had, if you know where to look. Jerash, an impressive Roman ruin, is about an hour's drive from Amman, and Petra, which is amazing, is about 4 hours south. I'd recommend contacting a good local travel agent and letting them arrange things. perhaps including a driver and a guide.