I can't decide which one is better to apply for mechanical or aeronautical engineering can you please help me.
With regards to Ivys, Cornell is your best bet for engineering, Princeton, and Yale not so much. And for aeronautical engineering, Stanford, MIT, Caltech. UT Austin, UI, Purdue, Georgia Tech, UMich., VirginiaTech. CMU and RICE are also excellent for engineering. Remember Ivy League colleges were never founded to be technical universities but Liberal Arts colleges that grew into research institutions with Graduate programs that have more specialties. Still excellent are RPI, WPI, and there are many I'm forgetting that are "Tech" or "PolyTechnical Institutes" like Cooper Union.
Neither are known for having good undergraduate engineering. Columbia and Cornell would be your best bets for an Ivy.
To keep this community safe and supportive: