Flying seems IMO the best option. One way flights start at around $220 (United from LaGuardia)
A bus like Greyhound is cheaper (starting at $140) but it'll take you more than 36 hours and you have to account for buying food and sleep & back recovery. 36 hours in a bus are no joke.
Train is not competitive both in terms of duration (40+ hours) and price ($250+). You could consider a sleeper but this are more expensive than a business class flight.
If you are really adventures you can research some of the "Chinatown busses" but I don't think this will help much in this case. (e.g. https://www.chinatown-bus.org/)
The cheapest option would carpooling. That works well in Europe (BlaBla car for example) but is still in its infancy in the US and splicing a trip like this together would require serious luck.