What activities can I do during my MechEng undergrad

…to improve my chances to get admitted to elite grad schools (MIT, Stanford, Harvard, etc…)?

Research.

Do you think research, in addition to an excellent transcript + excellent GRE scores, is enough? Or does the research need to be world-class?

Research is research. Though the reputation of your mentor might have an impact on admission, if a great rec letter is provided, the important thing is what you get out of it and how productive you were coupled to a great letter from whoever mentors you, of course.

I must say, an excellent record is NOT enough to get you into an “elite” school. You must legitimately be interested in the program, the school, and the professors rather than just reputation.

I know many people that go to “elite” colleges that got rejected from schools with less prestige because of poor fit with the school. Conversely, I know many people with great credentials that got rejected from “elite schools” because they didn’t have good reasons to apply besides prestige, or didn’t have enough research experience.

Why do YOU want to attend an elite school?

(Also, what schools are you considering elite?)

Harvard isn’t exactly an elite mechanical engineering program. I wouldn’t get so hung up on the “name brand” of the school and instead look at who is producing high-quality research in the area you intend to study in graduate school (as in the specific research area, not just “mechanical engineering”). The best way to measure that is by looking in the relevant journals and looking at what sorts of programs are publishing (preferably often) in the top journals in that field. It’s much more important that your graduate advisor is good than the name brand of the school.

Otherwise, @Bioenchilada is correct. The name of the game for graduate admissions at top schools is research, research, research. Even if it isn’t top level research, it is still very helpful and the strong recommendation letter you should get form that faculty member will carry you a long way in the admissions process, especially if that person has a good reputation in the field and/or strong connections at a given school.