It depends on how seriously you want to take it and what level of technology you want to use to compete. Here are a few basic levels of cross-country car prep, and then consider the costs associated.

1: Good Car add GPS, Radar Detector ($800)
2: add CB Radio, upgraded headlights (if not already great) ($400)
3: Better Car add police scanner, laser jammers ($900)
4: add fuel cell, you better have great brakes if you are getting to this point ($400+)
5: add thermal imaging system, make your car look like an ambulance, whatever... (how deep are your pockets?)

A night in NYC prior to the event= $150
A night at Portofino= $270
Gas= it's 2800 miles, I'll let you figure that one out
Going balls-out non-stop for real= Priceless