Just as Ponyville was established by Ponies, for Ponies, Centaur Dale was established by Centaurs, for Centaurs. All commonly known variants are seen trotting along the streets of the village.
The Mayor is basically a formality for ceremonial and ritual purposes, but she still do have an important role to play. The Queen is signing important papers, the one Go-To in the village.
Naturally, all vital functions are available, such as Café, food store, library, school and a dress shop. Would have been a poor existence without these institutions.