The ideal is to do really well at an Ivy league or very competitive school. I think it's harder to get really good grades at a State U. than at a Stanford/Ivy (having been either a student or on the faculty at both types).
I wonder if it depends on the type of course, but my husband would disagree and has a direct head to head comparison. He lived in a state where he was able to take college courses at State U as a high schooler (a State U that is considered to be academically rigorous and respected nationally). He then went to an Ivy for undergrad. Said it wasn't even close in terms of how easy the State U math and science courses were compared to the courses at the Ivy. He was able to fly through his assignments for State U courses often on the bus home, whereas his Ivy courses literally had him up against some of the top students in the world in certain subject areas and he had to spend hours/nights/weekends to achieve good grades.
I am apparently the only contrarian in this bunch, as I pointed out earlier that my undergrad at the University of Kansas (KU) was much harder than grad school at MIT.
I will expand on this because it's related to the cost of university education. At least back then, KU competed for students by showering them with scholarships. I received enough to cover tuition, room, board, and had spending money left over. I was also accepted to other schools including Caltech (but not MIT) for undergrad, but that would been a pretty significant hardship on my parents, so the choice was pretty easy at the time.
The honors cohort I took most of my classes with was easily stronger than most students I saw at MIT. Those that went to grad school after KU ended up at places like Stanford, MIT, Cornell, UPenn, etc., so from that perspective there was no disadvantage. In my opinion, the only difference between a good state school with an honors track and an elite school is with the first set of job opportunities right after school. There are a number of companies that only recruit at the elites, which I learned about after MIT.
If finances are an issue, as they were when I grew up, you can do far worse than accept full ride scholarships at a good public/private school with a good honors program. Just don't expect it to be easy.
