lawrenceville student here, so i will try to sell you on l'ville!

let's go through your list. just some background info, i'm also an asian female and i'm a new sophomore here right now!
- Rigorous academics
there is no doubt that lawrenceville is one of the top schools for academics, we have advanced classes and tons of options for anything you want to take.
- Large endowment (FA available for int'l applicants)
FA for int'l applicants will be difficult at any school but definitely a lot of people are on FA here, especially if you're recruited for a sport.
- Would like to avoid the 'snobbishness' or rich-kid atmosphere as much as possible :[
there is no such thing here, i can guarantee. yes people do tend to dress nicely, but no one judges you and almost no one is outright snobbish - of course there are those one or two people everyone just shakes their head at.
- Freedom for students; better regulations
i don't really get this one, but we have a lot of freedom here unless you're a freshmen. you can go off campus as long as you ask your housemaster and sign out/sign in, you manage your own time, etc. lights out at 11:15 every night except saturday and check in (after this you have to stay at your house) at 8 every night except saturday
- Great girls' basketball team =P
i actually don't know much about this, i'm not an athlete at all, sorry! but all the athletic teams here are amazing
- Would prefer something closer to a city, rather than total isolation
we are about 10 minutes away from princeton, which isn't really a city, but trenton is about half an hour away, philly is pretty close, and new york city is only 1.5 hours away!
hope this helped, feel free to message me if you have any other questions!