One of my all-time favourite places in Bangkok has to be the Old Siam. I can't remember if someone introduced me to the place or if I stumbled upon it myself during one of my many sojourns to the City of Angels.
The main attraction at the Old Siam, for me anyway, is the Food Hall. Here, they make, on the spot, all kind of Thai desserts and snacks. One can watch how all the food is being made and then purchase them.
What I normally do is purchase the stuff I like, which includes mieng kam (already wrapped!), other nibbles which I don't know the names of (but I certainly know the taste of!) and take it all upstairs to the Food Court. There, I normally order the oyster omelette, some som tum (papaya salad) and cha yaan (Thai iced tea) and Im ready to enjoy a great meal!
After my meal, I'd go down to the Food Hall again and there's a stall at the end that sells durian with glutinous rice and other very, very delicious (and extrememly sinful, with all that fatterning coconut milk!) desserts. There are some benches nearby so you can order and devour the desserts on the spot!
After feasting, you can feast your eyes with some window shopping. Many stalls selling Thai silk (around Bt350 per metre, very good price) and there's an electronics place upstairs. If you're getting married, you can make your invitation cards there and there's also a shop selling all the stuff for a Siamese themed wedding.
The Old Siam is definitely NOT a place to miss out if you visit Bangkok.
The Old Siam Shopping Center
Burapa Road
Pharurat / Chinatown area