- ο καφές = the coffee (nominative)
- τον καφέ = the coffee (accusative)
The nominative case is used when the noun is the subject of the sentence (for example "Ο καφές είναι ζεστός" = "The coffee is hot") & the accusative case is used when the noun is the object of the sentence (for example "Πίνω τον καφέ" = "I am drinking the coffee").
I hope that this helps. :-)
το καφέ: the color brown
ο καφές: coffee
From what I see now the etymology of the color καφέ comes from the drink, in its French version (café). https://en.wiktionary.org/wiki/%CE%BA%CE%B1%CF%86%CE%AD
If by café you mean the place where you can drink coffee, the most common word is καφετέρια (kafetéria).
Also the place where the old people go for a coffee/ouzo/to play cards is called καφενείο (kafenío).
A very common (and informal) phrase is "Πάμε για καφέ;" or "Πάμε για κανά καφέ;" (Fancy a coffee?).
The two versions are pretty close. The second is more relaxed, and vague, like time isn't an issue (it could be tomorrow or in 2 days).
The first is more urgent, and means "now", or within the day. But then, things are flexible in respect of time in GR...Depends on the person.