All organic (delicious) food with a fantastic view of the city and the citadel.
Take a stroll down Rainbow Street and pause at the overlook.
Take a bus from the North Bus Station to Jerash and spend a few hours leisurely walking around the ruins. Get lunch from a shwarma stand.
Return to Amman on the bus and visit the citadel in time for sunset.
Have a yummy yet cheap dinner downtown.
Participate in Amman's cafe culture. Go to Jebel Luweibdeh and choose from several cafes in the area to hang out in. Browse the neighborhood's artsy shops.