There's this thing called the top 10 percent rule in Texas. It's a bill that stipulates any Texan who graduates in the top 10 percent of their high school gets admitted to any publicly funded college in the state. The bill is a landmark law that narrows in on ethnic and geographical diversity.
There's certainly debate to be had regarding whether or not upward mobility is actually a thing, but this law draws credence to that code. You can at least be admitted to a top college, so long as you do well enough in high school.
Paying for school is another thing, but attending college at a prestigious school in Texas is considerably cheaper than it is in New York, even if you cast aside the cost of rent.