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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.

This is now my first stop when searching for basic boundary shapefiles (state, county, town), USGS raster data, and TIGER data (2003). I'm not sure who runs this site but the simplicity and open licensing are greatly appreciated!

"Datamob highlights the connection between public data sources and the interfaces people are building for them. Our listings emphasize the connection between data posted by governments and public institutions and the interfaces people are building to explore that data."

There is a wide selection of innovative maps, datasets, and data visualization interfaces drawing on a variety of topics. You can spend quite some time going through the offerings here!

The US National Atlas website offers dynamic, interactive thematic maps, multiple map generators for creating your own custom maps based on available government data, as well as raw data available for download by GIS professionals.

The Library of the University of Arkansas has a very impressive collection of international and US geodata repository links - mostly geospatial data and attributes.  I'll be poking around in here for hours, I think!  A wide variety of topics and well-organized to boot.

A project of Columbia University, "SEDAC’s mission is to develop and operate applications that support the integration of socioeconomic and earth science data and to serve as an “information gateway” between the earth sciences and social sciences."  In addition to a host of interactive mapplications, they host a large number of academic data sets on a wide variety of topics.