Translation:There are few stores near my house.
I think there is a big difference between "there are a few shops" and "there are few shops". To me, the former is more about stating that some (though not many) shops are there, while the latter is for emphasizing the fewness of the shops. I would translate "there are a few shops" as "ci sono alcuni negozi".
Granted, I am a beginning Italian student, so there may be a big difference between the statements in Italian. But in English, that distinction is quite subtle.
Just out of curiosity, why does mia go after casa in this sentence? I'm used to seeing it before.
"vicino alla mia casa" would work, but "a casa mia" is a common idiomatic expression.
“casa mia” refers to my home or my house in the sense of where I live. “mia casa” refers to the physical building.
Why isn't it Ci sono pochi negozi vicini a casa mia? I would have thought that since the location describes more than one store that it also would have been plural.
Because "vicino" in this case is not an adjective modifying a noun, it's an adverb used with "a" and meaning "near". "Vicino" as an adjective would translate better to "close", e.g. "vai ai negozi vicini o quelli lontani?" It's also used as a noun to mean neighbor.