How are they going to get there? This seems to be a pretty big point of contention between the siblings when they set out on their adventure, and it comes up again and again. Will they walk? Take the bus? Get on a subway? Or will they do what sounds completely ridiculous and irresponsible to Jamie—ride a taxi?
The whole transportation issue represents the difference between the ways in which Claudia and Jamie see the world. Claudia enjoys nice things and comfort. She's a girl with high standards, and so she thinks she should be carted around in limos and waited on hand and foot all the time. Jamie, on the other hand, sees the money trickling away:
"Claudia," Jamie said, "you are quietly out of your mind. How can you even think of a taxi? We have no more allowance. No more income. You can't be extravagant any longer. It's not my money we're spending. It's our money…." (3.5)
He knows how much money they have and is realistic (and stern) about how they should spend it. So, if they can walk, they should walk.
The transportation is also symbolic of the kids' freedom to escape and make their own choices. They may be just kids, but they're free to take the school bus (while hiding in it) to the end of the line and escape. They can get on the subway and make it to the Met. They can even walk wherever they want to do whatever they want. If they can get themselves places, then they have all the independence that two little runaways could dream of.