Welcome aboard the RoadTrip America forum.
It's about 2800 miles from Los Angeles to New York by either of two major routes. The southern route crosses the Southwest on I-40 and then cuts across the Midwest on I-44 to St.Louis and then I-70, finishing up on I-78 into New York. The northern route heads up I-15 into Utah and then follows I-70 over the Rocky Mountains, cuts up on I-76 to join I-80 across the plains and through the cities of the Great Lakes region and into New York. There is less than a 10 mile difference in the two, which you choose will depend on what you want to see. Have a look at one of the on-line mapping sites that we recommend to get an idea of what's along the way
AZBuck