late-night coffee shop
A coffee shop or kissaten that operates late into the night, often past midnight. The term emphasizes the late hours rather than a 24-hour operation.
See also: 喫茶店
I read a book until late at night at a late-night coffee shop.
喫茶店 is a general coffee shop or kissaten, while 深夜喫茶 specifically refers to one that is open late at night.
Compound of 深夜 (shin'ya, 'late night') and 喫茶 (kissa, 'coffee shop'). The exact historical derivation is uncertain, but the term is a straightforward modern combination.