Maya cities would certainly be surrounded by maize fields. Their absence from a reconstruction of a city probably has more to do with avoiding extraneous detail than any larger statement about Maya social organisation.

As for the actual techniques used, well the Maya had a lot of them. Much like many other American civilisations, the Maya practiced polyculture, the particular Mesoamerican variant known today as the milpa. In areas with less population density the Maya used slash-and-burn agriculture, also known as swidden. This form of agriculture can be productive. However, due to soil exhaustion, the land has to be rotated through fallow after a few years, and consequently it needs a lot of space. So, not ideal for large cities. Fortunately, the Maya had a lot of other techniques they could use. These included terraces, irrigation canals, raised fields, and bajos, or man-made swamps that could be harvested for fertiliser. In addition, they had several other types of farming, such as silviculture (tree agriculture) which helped them to maximise space. In fact, silviculture was so prominent among the Classic Maya that it is possible to identify where Maya sites used to be simply by looking at the tree species. If you find a lot of fruit and nut trees, there is a good chance a Maya settlement is close by.

Sources:

Acuña, Helga Geovannini, Rain Harvesting in the Rainforest: The Ancient Maya agricultural landscapes of Calakmul, Campeche, Mexico, (Oxford: Archaeopress, 2008)

Donkin, R.A., Agricultural Terracing in the Aboriginal New World, (Tucson: University of Arizona Press, 1973) Fedick, Scott L., The Managed Mosaic: Ancient Maya Agriculture and Resource Use, (Salt Lake City: University of Utah Press, 1996)

Flannery, Kent V., Maya Subsistence: studies in memory of Dennis E. Puleston, (New York: Academic Press, 1982)

Killion, Thomas W., Gardens of Prehistory: The Archaeology of Settlement Agriculture in Greater Mesoamerica, (Tuscaloosa & London: The University of Alabama Press, 1992)

Lentz, David L., Dunning, Nicholas P., and Scarbough, Vernon L. (eds.), Tikal: Paleoecology of an Ancient Maya City, (New York: Cambridge University Press, 2015)