As an international applicant, you will be competing with other internationals for limited admissions spots. Not asking for financial aid is a huge plus, and applying under an early decision program would give you a further boost.
The downside for you is that colleges use international admissions to encourage diversity (though only Americans are counted in the official diversity statistics). Coming from an English speaking, economically developed country and an affluent economic strata won’t exactly be a negative, but it’s not a positive either, moreso if you are White with Judeo-Christian heritage. There’s a lot of competition in this demographic, so you have to think about how to differentiate yourself in your application.
Your excellent grades and scores will get you into the competitive pool, but in order to stand out among other high achieving internationals you’ll need to present a compelling non-academic narrative as well. Selective colleges in the US put a lot of emphasis on life stories, extracurriculars, activities, talents. So think about what you can contribute to the campus community and then figure out how to communicate that in your application.
Any one of dozens of medium sized private universities and small liberal arts colleges would fulfill your wish list. Though colleges differ in environment and culture, you will find serious, thoughtful, intellectually curious students at all academically rigorous selective schools.
The best way to understand the individual personalities is to visit. If that isn’t possible, then it’s more of a hit and miss investigative process conducted on-line. Look carefully at the statistics for international admissions and think about what could make them choose you out of the crowd. You may have to cast a wide net and apply to 10 to 15 schools.
The system of identifying reach/match/safety is more of an art than a science, especially for internationals. You many prefer to concentrate on reaches and matches and use UK universities as your safeties. It’s hard to get solid figures on acceptance rates for internationals. As a general statement the acceptance rate for internationals is considerably lower than the acceptance rate for US citizens. So when you make your list choose super reaches (e.g., HYPSM) sparingly and load up on the next tier of reach to high match.
My (very subjective) list for you would include Macalester, Carleton, Grinnell, Smith, Amherst, Williams, Swarthmore, Haverford, Reed.