Once we get down to the level of neighborhoods, below the township scale, finding GIS data can be very tricky. Neighborhoods usually aren't officially recognized, at least not by any body large enough or interested enough in creating accurate GIS data descriptions beyond "the houses between East Smith Street and the river."
Online real estate firm Zillow has created this collection of 7000 neighborhood shapefiles and associated geodata. They're under a CC BY SA license so you can use them on anything as long as you credit Zillow and share them along.
Movesmart.org is a new website and nonprofit organization dedicated to helping housing seekers find neighborhoods that meet their needs while at the same time promoting diverse, healthy, and vibrant communities. The organization's core offering is an interactive mapping application called Neighborhood Finder (launching late summer 2009), which provides a geographic interface to many different types of data about neighborhoods. Other resources include a series of informative guides about relevant housing and neighborhood topics and a blog about fair housing and other similar issues.
You can learn more about Movesmart.org, as well as watch a short video about the organization and the website, by visiting http://movesmart.org/about (new window).