Does anyone know of a reliable source where to download city/town polygon shapefiles? I'm specifically looking for NY and NJ. I have come across point shapefiles, but not polygon. For example in NY there are towns like Hicksville, Syosset, Bethpage, Jericho etc that are contained in the town of Oyster Bay. I'm not looking for the Oyster Bay polygon shapefile (NYS clearinghouse has those), but of polygons delineating each of the former smaller towns. I've checked the Census Bureau but can't seem to locate anything either.
Run a search for "GIS data download" and the county the towns are in. The majority of counties with a GIS presence have a simple polygon shapefile for this. It will generally be called municipalities, jurisdictions, or could be split into parts such as townships, villages, and cities. Many counties have web portals where information can be downloaded. If you see a county has a GIS department and doesn't have a website contact them and see if there is an alternative way to obtain the data (often a FTP site).
I would check to see if the city has GIS data as well. From my understanding in NY towns are made up of multiple incorporated entities such as villages.
Zillow maintains neighborhood boundaries, however they are limited to large cities. A compromise might be to conflate the neighborhood data and Census-designated places. For the gaps in that coverage, you could use Thiessen polygons generated from the placename point information you've already identified and work from there. There's also ZCTAs from the Census, and as most zip codes have one or more names associated with each, you could build out place names from that, as well.
If you're actually looking for civil boundaries, NJ's 565 municipal boundaries are available from the state's data clearinghouse, NJGIN. New Jersey has 21 counties and no unincorporated area, so those 565 local governments would provide a complete coverage. Local governments in NJ are not nested, like Towns and Villages in NY. The municipality data, however, will not include names like "Iselin", "Journal Square", or "Vincentown", which are simply place names/neighborhoods within Woodbridge Twp, Jersey City, and Southampton Township, respectively. The upside is that Iselin would be in the CDPs, Journal Square in the Zillow data, and Vincentown in the ZCTAs (as 08088).
You can use the site Global Administrative Area. There, you can find surfacic shapefile for each country. Each country is divided according to its administrative divisions (ex: provinces and major cities).
I am not certain that you can find a polygon for every city though.
I would look into the US Census 2015 Boundary Annexation Survey. These contain Minor Civil Divisions (MCD's) submitted at the County level. Very up to date and accurate. I'm not sure about the actual places you mentioned, but if they are cities or villages they will be in there. If they are just unincorporated Census Designated places (CDP's)they will not have established boundaries. CDP's are only delineated by residents saying that it is where they are from.