What kind of car is Tom Cruise driving in the opening scene of the
movie Vanilla Sky?

Hello.

It's a Ferrari 250 GTO replica.

"At the beginning of the Hollywood movie Vanilla Sky, Tom Cruise
drives a black Ferrari 250GTO through the deserted blocks of New York
City."
source: classicdriver.com
http://www.classicdriver.com/uk/magazine/3200.asp?id=12207

From Motortrend magazine:
"Ferrari Scrapbook
Vanilla Sky" (2001; 250 GTO replica) 
http://www.motortrend.com/features/consumer/112_0409_ferrari/index3.html

"The other car David Aames drives is a Ferrari 250 GTO."
source: cameroncroweonline.com
http://www.cameroncroweonline.com/films/vanillasky/secrets.htm


"It's true that Tom Cruise/David Aames is MEANT to drive, in the
initial scenes of Vanilla Sky, a Ferrari 250 GTO, but ... it's a fake
one !! Cruise revealed this ""secret"" on national TV to David
Letterman, January 2002. He said that only two original Ferrari 250
GTOs are left nowadays, and obviously their owners didn't want to lend
them to the producer (Cruise himself, together with his producing
partner Paula Wagner) of Vanilla Sky. So, they ""masked"" some other
model of car - he didn't specified which one it actually was - to make
it look like a Ferrari 250 GTO."
http://www.ultimatecarpage.com/frame.php?file=car.php&carnum=134

--------
search strategy:
"vanilla sky" ferrari
"vanilla sky" ferrari 250

I hope this helps.