This construction is exceptional, rarely used because it’s intended for a special effect; it is used to make it clear to someone that a rule or a way of life is quite différent from what they’re entitled to expect or what is usual or simply what they expect because of their particular outlook on life while reality is somewhat different. It is a way to say “and that’s that”, “there is no more complication about it”, “as harsh or difficult or strange as it may seem there is no other way”, or again “you’d better do it that way as there is none other”.
I can’t tell about the register of this construction; I do know it is used with the pronoun “vous” instead ot “tu”; it might not do in formal writing, though.

In Atlanta, you buy your coffee in the street and you drink it in the street and that’s that.

• that’s that (Oxford dictionary) colloq there is no more to be said (or done), the matter is settled, closed, finished, etc.

As cl-r commented, a properly punctuated sentence would be:

À Atlanta, c’est : « Tu achètes ton café et tu le bois dans la rue ».

C’est can be removed from the French sentence without changing the meaning:

À Atlanta, tu achètes ton café et tu le bois dans la rue.

Here, the rôle of c’est is to introduce a clause describing the way things go in Atlanta. The sentence can be translated by :

In Atlanta, the practice is to buy a coffee and drink it in the street.

or

In Atlanta, you just buy a coffee and drink it in the street.

C’est is proper spoken French just like y’a.

Here is an example of this usage of c’est:

La création, pour moi, c’est : tu prends des gens et tu fais avec les matières que tu as en face de toi.

Pierre-Emmanuel SORIGNET, Danser, enquête dans les coulisses d’une vocation, 2010