does 'szomszéd' have 'next' meaning?
I would say it has the meaning "adjacent" or "neighboring" when it is used as an adjective. That can be interpreted as "next" when you have things in an orderly arrangement, like streets.
If it helps at all, it's cognate with Russian сосед (as a noun) or соседний (as an adjective), and behaves pretty similarly.
In Polish "sąsiad" (as a noun), "sąsiednia" (as an adjestive). "Sąsiednia ulica" = "szomszéd utca".