Khan Al Khalili is the biggest shopping area with bargaining for everything. It is very crowded and noisy and I chose not to go there after the discoveries I made where I did shop.
Most of the shops along the streets will allowing bargaining to an extent. Usually, this means an extra item will be included or a discount for multiple purchases. Just about every shopkeeper offered me tea, coffee (Turkish), or soda before and/or after a purchase. This is rather a custom and considered rude not to accept. I did accept and drank as I was browsing and sometimes enjoyed a cup after I made purchases just to chat.
I feel it is a good idea to browse these shops before deciding to go to a place like Khan Al Khalili. You will be better prepared about prices and quality. And in all places, to say you are just browsing doesn't work. Every item you glance at they will tell you about and/or offer a good deal to you.