NOT Bais Shraga.
Good school but definitely yeshivish, discouraging college (they’re not allowed to take the SAT).
(But we’ve had the yeshivish-or-not discussion already 🙂 )
Shaar HaTorah in Queens? I don’t think it’s super yeshivish at this point, and it seems to be fine with college, considering it offers APs.
EVERYONE EVERYWHERE will use the word geshmak.
Unless you’re looking more for a yeshiva high school like MTA? Can’t really tell from your post.