You will probably end up in the Raghadan area, because this is where the Roman ruins are. Once you're done seeing the very exciting ruins, you may want to stroll around and check out the hundreds of tiny shops selling touristy stuff. Go ahead, but be forewarned -- this is the seediest area of Amman, and it is going to be here that you get your butt pinched or your wallet stolen. Travel in groups, dress conservatively, and keep a low profile.
Don' t expect all sunshine, Amman is quite high and this snowstorm occurred when i was there, so be prepared