I am an ASP.NET web developer (both VB/C#) and I want to create a web
page where, onload, a script will run that will query the
local.google.com database and return an array of every golf
course,address,city,state,and zip in the United States.

To further explain, say I was writing a SQL statement.  The
pseudo-code would look something like this:

SELECT Name,Address,City,State,Zip FROM local.google.com
WHERE What="Golf Course"


I don't need the code written for me or anything, I just need to know
a) if this is possible, b) which GoogleAPI I would use to accomplish
this, and c) (optional) a shove in the right direction, such as a URL
with this sample code, or a website that currently does this, or
suggestions, or whatever.

a) It is possible
b) You can store the coordinates in database and search for them
  The procedure is to
1. Geocode all the Golfcourse manually 
://www.google.com/apis/maps/documentation/#Geocoding_Etc
Usually you will be using host of polygons to represent a golf course
perimeter, which would be something like this..

var polyline = new GPolyline([
    new GLatLng(37.4419, -122.1419),
    new GLatLng(37.4519, -122.1519),
    new GLatLng( 37.4619, -122.1819)
], "#FF0000", 10);
map.addOverlay(polyline);
Check also ://www.google.com/apis/maps/documentation/#Marker_Manager

2. Then you can store the longitude and latitude info along with name
in your database.
  You can store '37.4419, -122.1419 37.4519, -122.1519 37.4619,
-122.1819' as varchar, and 'XYZ Golf Club' as string to represent your
golf club. Also you can add more information as in
://www.google.com/apis/maps/documentation/#Geocoding_Structured

3. You can show all golf clubs like the example in
://www.google.com/apis/maps/documentation/#Marker_Manager_Offices

Also, you can use search like 
://www.google.com/uds/samples/places.html

Query like 
SELECT Name,Address,City,State,Zip FROM local.google.com
WHERE What="Golf Course"
is possible.. 
You should be able to generate on the fly xml based on the query for
the required golf course and do something similar to example in
://www.google.com/apis/maps/documentation/#Using_XML_and_Asynchronous_RPC