Morpork is the half of Ankh-Morpork widdershins of the river Ankh.
It is not necessary to say "downtown Ankh-Morpork". Morpork is downtown. It's down in every category known to sociology and political economy, down geographically, financially, aesthetically and morally. Ankh has mansions and parks; Morpork has abattoirs and tanneries, warehouses and cathouses, dingy taverns and, below all, the Shades. It's also, overwhelmingly, where Ankh-Morpork's work is done. It contains most of the industry, commerce and shipping that support a city-state with no natural resources beyond a barely navigable river. It also includes Unseen University, the Patrician's Palace and the halls of most of the ruling guilds, so while the old-money aristocracy and the guild leaders may reside in Ankh, the power and control are exercised in Morpork.
Most of the locations for the many books about or including Ankh-Morpork, apart from Pseudopolis Yard and the Ramkin mansion, are in Morpork. This is because it may be dirty, evil-smelling and dangerous, but it's always interesting.
The city shares its name with an owl native to the Foggy Islands. No one knows why.
The Online Mappe
There was an extremely good interactive map of Ankh-Morpork on the French-language Discworld site Vade Mecum: unfortunately, the Vade Mecum site is no more. Only a Twitter account remains.