Honestly it's a pretty hard calculation to do. You don't know what colleges are going to cost on average by the time your kid goes to college (assuming he or she does in fact go to college...). You also don't know if your kid will end up at an expensive private school or a cheaper public school.
And, how much aid, if any, you will receive.
College tuition has risen dramatically in the past decade (perhaps longer?). I can't fathom how this is sustainable. But who knows how long that will last?
So yea, what I just said wasn't particularly helpful. But here's what I do know:
1) Don't worry about the scholarship thing. If your kid gets a scholarship, then you are allowed to withdraw the amount of the scholarship penalty free (but not tax free).
2) If you aren't already aware, 529 funds can be used for room and board. The amount you can claim for tax free use of 529 funds is the greater of
a) amount actually charged by the school
b) the cost of attendance figures for financial aid published by the school
Notice how if a student lives off campus, it doesn't matter how much in room and board expenses your kid incurs, you can always pull out that published amount in #2 tax free.
I sampled yearly cost of attendance figures for room and board for a handful universities that popped into my head:
Cornell:$13.6k
UIUC: $11k
UMCP: $10.8k
Georgia Tech: $13.1k
Univ Minnesota: $8.7k
Let's take the average (I realize we have only 5 sample points here, but the room and board figures are mostly a function of cost of living of the area, so hopefully they won't vary too much unless we're talking about particularly HCOL areas): $11.4k
So assuming that these 5 samples are actually representative of the pool of schools your kid would apply to, that would mean you can withdraw $57.2k (4 years worth, in 2015 dollars) from the 529 tax free.
Now let's assume your $120k grows at 3% faster than the room and board costs? I'm guessing you're going to have this invested more conservatively as your kid gets closer to heading off to college, so the returns wouldn't be too high.
That would give you $152k
Assuming your $152k only grows with inflation (and I don't mean CPI, but college expenses inflation) after that, that means you've got $57.2k you can withdraw tax free over four years for room and board, leaving you with $100k for tuition.
I made some assumptions above that you can adjust to your own liking. I don't really have a grasp for what assumptions to make. But you can at least look up the cost of attendance figures for schools you want your kid to consider (of course, whether your kid may actually want to go there is a different story...)
Oh yea and honestly depending on your current tax bracket, withdrawing money when you've retired with the 10% penalty may not even be all that bad.