Jhalana-Amagarh Leopard Conservation Reserve is the wildest thing you can do without leaving Jaipur's edge. The dry Aravalli forest supports leopards, nilgai, jackals, and birdlife, and guided jeep safaris make it a very different counterpoint to forts, bazaars, and palace courtyards.
Sightings are never guaranteed, which is exactly how it should be. Go for the early or late light, keep expectations realistic, and treat the reserve as a rare chance to see how wildlife survives beside a large Indian city rather than as a zoo-style leopard appointment.