Beyond the obvious private schools (Cal Tech, Cornell, MIT, Princeton), most of the big state schools offer overall solid and broad-range engineering programs. U of Illinois to U of Iowa, Indiana, Texas Tech, Ohio State, North Carolina to Iowa State. State schools like U of Michigan, Illinois, Cal-Berkely rank up their with Stanford.
In short, getting into a big state school is a great start for a normal person, from U of Texas to Northern Illinois. Clearly, if you get a full scholarship to Princeton you're doing okay
For the record, my dad was an engineering professor at the U of Michigan, which probably ranks top 5 overall, and he's high on state schools. He got his Ph.d. from the University of Minnesota. Though my dad grew up in a blue collar middle class family-- his dad was a train worker-- and would say sending your kid to U of Wisconsin or Virginia was just as good as sending him to Yale. As an engineer, he was practical about things. Of course, back when he was a professor, state schools were affordable. Often different today.
There are only a few MITs and Stanfords in the world, but there are a lot of reputable and decent engineering colleges for the normal guy-- perhaps one in state.
Also, my dad retired numerous years ago and spends most his time now doing crossword puzzles, working in the yard and walking his dog. Engineering rankings is about last on his mind.