Mamod; there are a few parks in Amman, they may not be exactly what you are looking for, but worth exploring:
1. Paris Square (previously named Alhaouz) in Jabal Al Weibdeh (sit and watch people)
2. The Lovers Park (the park where the National Gallery for Fine Art is located) in Jabal Al Weibdeh (sit and watch people)
3. King Hussain Gardens (where the Children's Museum is located) Military Medical City Street, the same street that has City Mall. (you can play ball there
4. Al Saha Al Hashmieh (you can play ball there)
5. The Amaneh (Ras El Ein) has a nice sitting area. (play ball is a little hard but possible, but definately sit and watch people)
6. i also saw one in Abdoun, two streets away from Jordan Kids Club or something like that. (there is a place to play ball, sit and watch people)