Many Mexican cafés are called La Parroquia, but the original one is in the port city of Veracruz, capital of the state of Veracruz.
The place is very easy to find: it is on the malecón, and it takes up half a block. There is both indoor and outdoor sitting available.
The espresso is made with old, huge Italian coffee machines. The typical thing to order here would be a lechero. There are waiters dedicated only to the serving of lecheros, and they run around in furious hurry with their two kettles.
One etiquette point to keep in mind is that in La Parroquia the only proper way to order a refill of your lechero is by striking the glass with your coffee spoon. Notice that anywhere else in Mexico this is a beastly act of rudeness, or a rude act of beastliness which would mark you as a rude beast.
Another interesting aspect of La Parroquia is its unique free enterprise system: waiters take your order, transmit it to the kitchen, pick up the order and pay for the order out of their pocket.
It is the same waiter that draws up the bill, and collects the money from you. I suspect that this gives the waiter a unique incentive to watch over you, especially at the outdoor tables.
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