If you want a farm/fishing town, don't hesitate to drop some mines, woodcutters and quarries among farms, slot in food bonus resources. When they grow larger, replace those with food and happiness boosting buildings, and turn liberated miners and woodcutters into farmers/fishermen. Buying a building adds a population unit. After that you suddenly have a larger town, now you specialize it for food and it produces a heap of food that's funneled into your cities for their growth. Intersperse a bunch of smaller and closer located towns in-between a few of your farther apart placed cities and they'll will grow into huge population centres, overfilling with specialists.
A lone city without town support will have to sacrifice some tiles for food production. It will struggle with growth and production. Having supporting food towns you outsource city's food production to those towns and then the city can build other stuff on those tiles, you can have more production buildings and build things even faster.
The same with production towns: after necessary growth is done, replace farms with production buildings in towns in production heavy area, specialize them into production and they will become cash cows for your empire. Cities are there to thrive on towns and towns are there to be milked by cities.