Is there a place that has neighborhood boundary data for Israeli cities as polygons?
I have searched the web without results.
Unfortunately, there isn't a freely available, nation-wide polygon layer. You can try contacting MAPI regarding their Cadastral data which might have neighborhoods, or the CBS/MoI statistical region layer. (If you don't know what these are, search for them on govmap) Other than that, your only option is a point layer with neighborhood names as found in Open Street Map.
Update: I asked around, the Ministry of Construction and Housing might have such a layer for some cities. Try contacting them.
Have you check this out ? http://www.diva-gis.org/gdata if this is what you were looking for ?