My area searches
To be clear, there is nothing official about the boundaries of these neighborhoods. Although these areas are generally known by names I'm using, these are not clearly defined subdivisions. You'll find a map defining each area on the linked page, and a save button on the top left of each page where you can sign up to receive notices when new properties come on the market in each area.
Downtown Subdivisions
You may think to yourself, how are "Other" and "Not in a Subdivision" listed as subdivisions. Not every property, particularly in older areas, is in a subdivision. These monikers were used by agents over the years to describe properties not in formal subdivisions and they still get used from time to time.