What would it cost me to ship my TV from Southern Calif. to Downtown
NY? It's a 36-inch flatscreen w/ a stand. (Sony XBR)

Here is the quote i got from PakMail: $558

They have an engine where you can type in specifications and get a
quote:
http://www.pakmail.com/quoteengine/

Here is the data I used (garnered from some info sites on the 36' XBR)

Dimension (in inches) 40x31x35
Weight: 235 lbs
Value: $1900
Sending Zip code: 10034 (Manhattan)
Receiving Zip Code: 90047 (LA)

If these zip codes are a little off, you can run the engine to get
more accurate results, but the price will probably be about the same.

Search terms used: "zip code" manhattan "los angeles"
sony XBR 36
shipping cost television

Oh, one thing I forgot to mention.  I realize that the above quote is
for the opposite route you wanted, but I couldn't get the engine to
work going the other way because it kepy rejecting my email addresses.
 I would think that the quote is still a pretty good rough estimate,
though.

I meant zip codes not email addresses