Route Reality
The United States is too large for casual cross-country planning, so a first route needs flights and clear priorities. New York gives the strongest city start, Los Angeles adds West Coast culture and California access, and the Grand Canyon creates a national-park highlight.
New York City
Spend at least three or four nights in New York if it is your first visit. Group sightseeing by borough or neighborhood, book popular viewpoints or shows early, and avoid changing hotels inside the city unless there is a strong reason.
Los Angeles
Los Angeles should be planned by area and traffic, not by map distance. Choose a hotel base around beaches, studios, museums, or nightlife depending on the version of LA you want. Renting a car can help, but parking and traffic need planning.
Grand Canyon
The Grand Canyon works best as part of a Southwest extension from Las Vegas, Phoenix, or a longer road trip. Book park lodging early, carry water, and plan around sunrise, sunset, and heat rather than only midday viewpoints.