<p>Best fit for you in any of the majors does not necessarily exclude either LACs or research universities (unless LAC or research university is one of your actual criteria). Presumably, the availability of subjects you want to major in is important, as is net cost.</p>
<p>Engineering does exist “natively” at some LACs like Bucknell, Harvey Mudd, Smith, and Swarthmore, although the latter three have everything combined in one general engineering degree program instead of specific degree programs for chemical, civil, electrical, mechanical, etc. engineering.</p>