A two hours drive from Amman you will find the historical site Umm Qais. It is a nice area and an interesting drive from over Irbid passing by green fields. From Umm Qais there is a nice view of the surrounding countries to the North and West and you can see Lake Tiberia. If you go to Spring it is very green. I recommend not to go on Fridays but Saturdays, as it will be less crowded. If you can, take the chance to grab a snack or coffee at the restaurant within the site. However, it might be busy so depending on when you go, reserve a table.
You might combine the trip with visiting Irbid, Pella, or Jerash/Ajloun or some other highlights in the North of Jordan. It is a great site to take friends who visit you in Jordan. Umm Qais is also the starting point for the Jordan Trail which is a hiking trail that runs throughout the whole country. When coming to, take the road near Irbid, when leaving take the Dead Sea Highway and turn towards Amman bypassing the road towards As-Salt. There is a cafe called Sunset cafe offering a stunning view over the Jordan Valley. Although It is not very fancy, you can sit outside and bring your own food.
Tourists pay 5 JD, residents/Iqama 250 fils.
Pictures of Umm Qais in April
Umm Qais in November