As we speak I'm listening to the Drone Zone ambient stream at
Soma FM. They've got several other electronica and loungy streams as well.
The WNYC public radio program
New Sounds plays a huge variety of "art" music in nightly 1-hour themed shows: ambient, world music, downtown NYC-type jazz and skronk, modern classical, electro-acoustic, laptop, etc. Several years worth are archived
here with full descriptions and playlists.
You can check out a bunch of of 20th century American "classical" composers (John Cage, Steve Reich, Aaron Copland, Duke Ellington, etc.) at the website for the public radio series
American Mavericks.
And there's always the ridiculously eclectic
WFMU, who archive all of their broadcasts, frequently with individual show
playlists and descriptions, all
searchable and
browseable.