Reality is much more complicated than my imagination.
Character runs away. She goes to the station, gets on a bus or train, and goes.
For the heck of it, I checked out the schedule, just to compare fares, and find out if there actually was a train that could do it.
There was... but the train doesn't leave until the next morning, she'd have to spend the night in the station. The bus requires three transfers, New York, Richmond, Texas, and would take four days. Long, miserable ride. --But she can't spend the night in the train station, she'd get caught. She'll have to board the red-eye bus to New York, get over to Penn Station at 2AM and then hang out until 6am when the train leaves.
A little look at reality complicates the story, gives lots of fun stuff to happen.