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Just for fun, I did some price-searching. Cary to NYC or Rocky Mount to NYC, both have the same "best price" of $156 for round trip. Rocky mounty has at least twice as many options, and the travel time is about two hours less (8+ hours instead of 10+). As noted before, Rocky Mount is likely the preferred originiation point.
I looked on Travelocity, and there are about a dozen flights or more for $196-197 for round trip, and about double that if you expand your price to "within $50" ($206). Direct flights are about 1:45, door to door.
Other considerations:
Baggage is free on a train
It drops you at Penn Station, so you don't have to take an $80 taxi, or $40 uber into town, maybe a $5 subway ride.
So if time is an issue, it's probably worth flying. If you can enjoy the trip, it's a nice way to travel, and savings add up.
If you have two or more adults, and if you can find affordable parking in NYC, driving is always cheapest. It's about 1000 miles, round trip. So even if you are driving a car that only gets 20 MPG on the highway, you are looking at around 50 gallons, or $130 (less if you fill up in cheaper states).
I based travel on Oct 17-21, just to pick a date, and gas based at $2.60 a gallon, which should come down by then.
Don't forget to add in tolls for driving, pretty steep. But still more affordable when you are figuring for multiple travelers.
I go from Cary to DC about twice a year. Other than a taxi to the station, its train > Metro > bus right to my Mom's house in Maryland. My favorite part of the trip is traveling through those small NC/VA towns where you are literally traveling right up Main Street.