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.
Address: Amman - downtown
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 (~_~)