@mydaywasgreat : Actually, you overestimate how small classes are at most private schools. If you did STEM (where usually introductory courses are the deciding factor for whether or not students continue) at Emory, it would be kind of exceptional for medium sized private schools as they usually even limit introductory courses (except physics I think) to something between like 70 and 120 per section. Instead of having a faculty member teach one section of 200+ (note that this range varies from 200-350 I guess) like at most of Emory’s peers (this is fairly close to many publics. Some publics have much larger sections though), they give key faculty members two section of 100ish (or less) so that they can do more than pure lecture when in class. Most privates in STEM are pretty classical (Emory isn’t because it was a regional teaching university until 1995 so tons of emphasis was put into maintaining size and quality of lower division courses. This exists today as well, albeit somewhat less than before). The primary difference is that in the first year, most privates give you access to small courses because they may require a seminar or writing course for freshmen. Also, most departments outside of STEM tend to be very flexible and have many smaller courses (you could be a freshmen that takes a seminar style course at the 200 or 300 level in some social sciences and humanities) with no pre-reqs whereas at publics, there are often rules that make access to such courses harder for freshmen (likely to restrict elective courses to majors).
Note that I said you should attempt to place into public school HONORS PROGRAMS. These will likely provide smaller classes, especially in STEM than most selective private universities. On the other hand, there is the option of LACs and LAC like universities. In addition, if you go to a public school with AP credit, even if you are not fully in honors program, you will be treated well and likely be able to use that AP credit to place into more advanced or honors sections which will probably be a similar level or better than the average class at a selective private, but just much smaller because a much smaller cohort of folks are pursuing that option. Furthermore, in most cases, even if you have to start with the large courses, the size will start dropping off at both privates and publics by sophomore year assuming all goes well and you begin intermediate and advanced courses in your area of interest.
I could go look for some schools at a similar caliber to Emory that are not super reaches, but I think most of the places I am thinking of are still harder to get into than Emory, just not super hard (I am thinking places like Brandeis, Tufts, USC, CMU).
*I want to make sure folks avoid painting this overly rosy view of education at privates vs. publics (it can be grossly exaggerated). Honestly some of the very top selective privates are really so good because they more so mimic the paradigm at publics. Lots of concentrations and specializations, and lots of advanced options for very ambitious students (like the tiering of introductory STEM courses at places like HYPSMCt, and Chicago looks more reminiscent to the amount of tiering seen at least decently resourced publics).