The medina of Marrakech is chaotic maze of narrow streets filled with people, racing motorbikes and carts pulled by donkeys. Everything is happening there and that's where you'll want to be. Most of the worth-going-to Riads - which are traditional Moroccan houses where you can stay overnight, just like a hotel - , cafes and restaurants are inside the medina.
As you get nearer to the souk - market in arabic - you'll notice that everyone will try to sell you something. It will be tiring sometimes but nevertheless, the Marrakech souk is an incredible place to go shopping for all sorts of artisanal products. From scarfs, to rugs and pillows, to woven baskets and wood pieces, to leather and metallic artefacts. You can also find a variety of spices and herbs, marinated juicy olives, shiny lemons, different kinds of dates and nut pastes. Just make sure you have your haggling skills prepared so that you don't end up paying triple the price you should!