Every specialized city requires a specific topography. Now I would like to give you some suggestions about what kinds of terrain are ideal for specific city types. As usual - a perfect terrain is a rather uncommon thing to find - so in most situations you will just have to use whatever you can find and make best use of it.
The Production City - a lot of hills, preferably forest hills and some grassland tiles, flood plains or (luckily enough) some Food resources. Strategic resources which are giving us Production bonuses - like iron, copper, stone or coal are extremely useful.
The Commercial City - a lot of grassland (possibly with forest) and flood plains. Some hills would be helpful, too. Luxurious resources are a nice addition, especially Gold, silver, gems or wine.
If your Leader has the Financial trait, the coastal city also can work as commercial city - with use of some nice commercial gains from sea tiles and really profitable sea trading. However, land city plays the role much better, even if it needs more time to develop.
Despite the type of city, you need to avoid situations when your commercial centre doesn't control any Production generating tiles. Even huge amounts of cash won't help if simple buildings are created in dozens of turns.
The Great People Factory - a lot of grassland near river or lake, one or two Food resources, flood plains. The key is to be able to support maximum number of citizens. With terrain improvements you try to maximize Food output.