As suggested, I am re-posting my comment as an answer, adding the comment from @DaG too.
"Negozio di caffè" suggests more the idea of a store selling coffee beans and powder rather than a place where you can order a coffee.
"Bar" indicates a place where you can order a variety of alcoholic and non alcoholic beverages (and often items like crisps, candies and the likes).
"Caffetteria" is used with two slightly different meanings (see treccani.it):
- it can indicate a place serving coffee (and cappuccino, latte, etc...) and sweet pastry (meaning 1/2 of the link) or
- it can indicate a place connected to a museum, university, station, etc... selling food and beverages (meaning 3 of the link)
Nowadays, the second meaning is probably the most used one, while for the first meaning the abbreviation "caffè" (see below) is more common.
"Caffè", which literally means simply "coffee", is quite often used as a short version for "caffetteria" (in its first meaning), but it is not uncommon to ear people using it to refer to a "bar" that serves coffee too.
E.g. «Andiamo a quel nuovo caffè in centro» («Let's go to that new coffee shop downtown»)
I also would add that the distinction between "bar" and "caffetteria" (in its first meaning) is not a clear-cut one; many bars are actually what we used to call "bar caffetteria", serving both bar and caffetteria products and virtually all of them serve at least coffee.