Right across the street from the Red Fort (and up a hill) is the Jama Masjid. This is the huge mosque Shah Jahan had built around the same time as the Red Fort. You must walk through an open air market to get to the mosque, and when you get to the entrance, there are sheisters there who will tell you that you have to leave your shoes with them. When you come out to get your shoes back, they ask you for an exhorbitant sum. If you act angry, they give you your shoes back for twenty rupees. Or, at least, that's what happened to me. Once I got into the mosque, I realized most people were carrying their shoes with them. The rules for the temples and mosques vary, though. At some of them, carrying your shoes inside can be a terrible insult, and I didn't want to risk it.
Like the Red Fort, the Jama Masjid is also made of red sandstone, which I realized after walking through it barefoot, is much like the stuff they make that Pampered Chef baking stoneware out of. The soles of my feet were so burnt that they stung for about two days afterwards. But I got some good snaps out of the deal.