Where to visit in Jordan? (Amman)

I would be visiting Amman on business. Would have 2 days free to visit places of interest (plan to visit Petra).

Would appreciate any suggestion on places to visit and love to connect with people.

I am a freelance writer and photographer (apart from my work in software) and my interests are in culture and music - saying this as context to suggestions for places of interest.

Have a splendid day.