The Strip closes to all vehicle traffic early in the evening on December 31 every year; it'll definitely be blocked by the time you get off the plane.
Meanwhile, the crowds are so huge on the Strip, and parking is so tight within a quarter-mile of it, that we strongly suggest you grab a taxi and give the cabbie a big tip to deliver you as close as you can get. You can worry about picking up a rental car on New Year's day (reserve early, though, as 250,000 other people will be in town, competing for the reduced fleet, which is why prices are up).
We also suggest you attend to your bodily functions at the airport. By the time you land, get a cab, and fight the traffic to the Strip, all the casino doors will be closed to non-guests and you'll need a room key to get in. Even if you have reservations and are trying to check in, chances are (unless you encounter an extremely cooperative security guard at the door) you won't be admitted till long after midnight. Which means you won't be able to hit a restroom till then either.
And dress warm. Think Times Square. It's cold late at night in the desert in December, usually in the 30s.
