For a small fee you can be guided around the Grand Mosque in Amman. Women are given a hooded abaya to wear and should dress modestly. You can visit the various areas of the Mosque and ask questions about Islam.
Amman of course has many mosques, one of which is on my Amman front page, and another here.
I have to admit I dont know the name of this one. Let me know if you do (~_~)