For most situations where you want to work as an aerospace or mechanical engineer (as opposed to finance or consulting or some such), choose a school that is ABET accredited for the major (schools with ABET accredited general engineering majors with mechanical or aerospace subareas may be suitable). Even the few high-prestige-in-engineering schools that have discontinued ABET accreditation for some engineering majors retain it for mechanical (and civil of course).
Stanford retains ABET accreditation in mechanical and civil engineering, even though it has discontinued ABET accreditation for some other engineering majors it still offers.