<p>For a web app I'm working on, I need to know the lat/lon of about 300 US cities.  I also need to know the lat/lon for every US zip code.</p>

<p>Does anyone know of a free source to get this information?</p>

Freebase
will likely be able to help you.
Here is New York
and it has Lat/Long.
The
Wal-Mart Expansion video
used Freebase to get it's data, and it sounds like you're doing something similar.