The Wild Jordan Center is the visitor centre for the RSCN (Royal Society for the Conservation of Nature), perched on a spectacular terrace in the First Circle area with views across the downtown valley to the Citadel. The cafe here is the best place in Amman for the view — a long terrace with tables looking directly at the Citadel hill — combined with reliably good food and a useful shop selling products made in Jordan's nature reserves (Dead Sea salts, dried herbs, handmade crafts from the reserves).
The RSCN booking desk here is also the place to arrange visits to Dana Biosphere Reserve, Wadi Rum, and other conservation areas. The coffee is good and the sandwiches are well-made; arrive around sunset for the best Citadel views.