Daniel Shoag and Stan Veuger say yes, but I am not so convinced.
It turns out that metrics of land use restrictions are correlated with restaurant quality, across cities. To cut to the chase, Los Angeles ranks number one on this index, and I can agree with that assessment in terms of food quality and also diversity. (Other good food cities, such as Miami, also rank high on the index.) Yet for the metropolitan area near L.A., food is generally best where the land use restrictions are least binding. Beverly Hills and Santa Monica have some decent fancy restaurants, but the real gems are to be found elsewhere, in fringes such as northeast Hollywood, Silverlake (gentrifying a bit too much these days, however), north Orange County, Monterey Park, and so on. Pasadena has hardly anywhere excellent to eat.
I would suggest an alternative channel of influence: urban areas with high inequality have both better food (see An Economist Gets Lunch, but basically imagine the wealthier people generating demand and the poorer people supplying cheap labor) and more building restrictions. The wealthier people decide to do something to keep the poorer people out of their neighborhoods.
I hate to say “correlation does not prove causation,” but…correlation does not prove causation.