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They met at a cozy cafe downtown.
They met at a small, comfortable restaurant that serves coffee and light meals.
a small restaurant or shop that serves coffee, tea, and light refreshments
She worked at a trendy cafe near the university.
She worked at a stylish small restaurant that serves coffee and snacks near the university.
The term is derived from French and is commonly used in English-speaking countries.
Note that 'cafe' is the standard spelling in American English, while 'café' with an accent is more common in British English.
From French 'café', from Italian 'caffè', from Arabic 'qahwah' (coffee).
In American English, 'cafe' is the standard spelling, while in British English, 'café' with an accent is also common.