As well as Petra(allow at least 2 days)-Little Petra is fascinating and was deserted when we visited 2 years ago. Other places-Mount Nebo near the Dead Sea, the Dead sea itself, Aqaba, Amman. The Desert Castles(on the road to Iraq!) are interesting but probably only reachable on coach tour. Jerash if you like roman ruins.....etc
Food ok-if on the tourist trail will be mainly buffets in the hotels, but local cafes/restaurants will do usual middle east foods + pizzas etc.
It really is an amazing place-can't wait to go back there!