I hope everyone realizes that you should not put any money into a 529 plan or taxable account unless you have already put the maximum allowed amount into all available tax-shelered retirement plans first. And paying down/off your mortgage should also take precedence over taxable or 529 plan investing.
Only if you plan to tap your retirement funds somehow (possible with a Roth or possibly a loan from a 401K) or your home equity via loans (which has a high interest rate) to pay for your kids' educations. Especially if you have a very low interest rate on the mortgage with the tax break that comes along with the interest payment (if you itemize), it doesn't necessarily make more sense to pay down the mortgage. And don't think your house equity is exempt from scrutiny by top colleges looking at your assets for paying for college...
Also, most 529 plans have a variety of options regarding investment risk. They aren't just a savings account with .1% interest or something like that. There are options like that within our plan, but there are also things like "age banded" options with a mix of stock & bond investments that shift as your kid ages. We don't have all of our college savings in 529s, but generally those investments have done quite well over the course of the 15 years or so that we have had them. Investing regularly (especially if you can front load) in a 529 is an excellent way to make sure you have money set aside for college. There are also ways you can get the money out if you don't need it for education for various reason without a tax hit (if your child gets scholarships that cover the cost, for example). Or it can be used later for a graduate degree if you want to. Or transferred to another person (child, grandchild, etc). Don't knock the 529 investment and assume retirement and mortgage paydowns are a better idea. They have their place as well, and we have not ignored retirement or the mortgage. But we are better positioned that almost anyone I know in our income bracket for paying for college, so take that for what it is worth.
Note that the net price calculators are not reliable if you have a small business, are divorced, get any money from relatives to help with payments, or have any trusts. They are not a guarantee of what your actual cost will be. I assume that to run the calculator for a state school like Berkeley or Michigan you need to tell them if you are a state resident or not -- the costs shown in 22B's list are clearly from OOS. And who would expect a state university to give good need based aid to an OOS student? So that is no surprise.
Regarding the question about USAMO -- no one can tell you what the admissions committee considers "worthy" of admission to any of these schools. A very top prize nationally in a competition like USAMO AND great grades AND great test scores AND great recommendations will certainly get your kid considered at top schools. But they could be competing against kids who have that AND play a sport AND are an under-represented minority at the school. There are no guarantees in this process.
And you can (honestly) destroy your relationship with your kids if you become a "tiger parent" who is all about admission to those schools and drive your kids to accomplish it. To me that would not be worth the tuition break... you might say you are not being a "tiger parent" because you are doing it for the money, not the prestige. But the end result for you and your kids is the same.
You asked about merit aid. Generally colleges that are "second tier" or lower tend to offer more merit aid. Merit aid is not based on your financial need at all. BUT, many colleges cut need based grants if you get merit aid. Some of them will cut the loans out of their financial aid "package" first if you get merit aid from the college. Note that outside scholarship also often offset the need based package. So your cost of attendance ends up unchanged...
My D got the following merit aid offers this past spring. All are "per year", so she have gotten this each of her four years on campus:
Kenyon - $15,000
Macalester - $15,000
Lawrence - $21,000
Mount Holyoke - $25,000 plus funding for a summer internship
University of Chicago - $5,000
She also would have gotten an extra $1,000-$2,000 per year for being a National Merit Finalist if she had picked any of those colleges.
There are colleges that offer free rides for merit -- University of Alabama and University of Oklahoma come to mind. USC has some half tuition scholarships for National Merit Finalists, too. Some public universities, especially in the south, have guaranteed scholarships for students based on test scores/GPA.
Really, we ARE recreating College Confidential out here. You should go out there and review the existing threads and post questions there. Here is a link to the financial aid forum:
http://talk.collegeconfidential.com/financial-aid-scholarships/ At the very top of this page there is a link on automatic and full ride scholarships.