Hi,
Can you please list any good private university with good/decent engineering school(ranking) that does not have crazily competitive admissions (MIT, Caltech, MIT, IVY Leagues,etc…)?
Thanks!
RHIT, RPI, WPI, Stevens, Clarkson?
http://college.usatoday.com/2016/11/18/top-engineering-colleges/
Rochester Institute of Technology (RIT)
Case Western
University of Rochester
Boston University
Lehigh
Bucknell
Northeastern
Carnegie Mellon
Johns Hopkins (still very selective, but not quite on the CalTech/MIT scale).
Union might be a desirable destination for you as well.
Lafayette (LAC, not University.)
What kind of engineering are you specifically looking for? That could make a difference
Villanova, Trinity CT, Catholic U, Wake forest and Miami.
In addition to the above …
Northwestern
Rice
Washington University in St. Louis
University of Southern California
Notre Dame
Vanderbilt
Tufts
NYU
Syracuse
IIT
Olin
Cooper Union
Harvey Mudd
Rose-Hulman
Embry-Riddle
(some of these are about as selective as most of the Ivies)
UIUC?
^Great Engineering (like most of the rest of the Big Ten), but not a private school. But i’ll take the handoff. 
OP, some of the very best engineering schools in the country are at state schools and most flagships (if not all…?) and even some non-flagships offer robust, fully accredited programs. Unless you have serious issues with public universities, it wouldn’t be a terrible idea to apply to one in your home state that offers ABET-accredited programs as a low(ish)-cost alternative.
Oh haha of course, my bad
Your other threads indicate that you’re an international student who’s a sophomore at a public university. I don’t know how difficult it is to transfer into engineering as a junior. Check each school’s website to make sure they take transfers before you apply.