Oh, I'm pretty natural too, I just am just as comfortable in this heat (screw Boston summers, but you're in NYC, which is worse) in knit sundresses and well-cut linen trousers as I'd be in jeans, in fact, usually more comfortable. I often go makeup-less.
But you want to be picked up, as I understand it, by a suave European guy with an excellent vocabulary. This sounds like you're not over your ex-boyfriend, but aside from all that, if you want to attract that kind of guy, you have to make an effort to not only know the right people (know anyone who's expatting where you're studying? usually a start) and to be able to make the right kind of conversations, but also to look approachable and attractive, so you may want to upgrade slightly.
The sugar thing is … well, I wouldn't do it, but I married pretty young and I never tried to pay rent in Brooklyn or Manhattan, so I'm not gonna judge … for them, it's your youth and naïveté that appeal.
If you just want to get laid, yes, you can do the club scene, but if you want real relationships, you'll have to have a lot on offer and that not only includes the physical component — dressing in flattering clothing, getting your hair right, and looking sexy and alluring while simultaneously like you made no effort whatsoever and you just happen to be wearing this because it's comfortable — but also the personality component, where you have lots of interesting things to say and can share informed, intelligent opinions and debate someone quite well.
That's going to limit you, most likely, to English-speaking guys, but depending on where you're going, that may not be much of an issue. Try meeting people online in that area who share some interests with you. The language exchange thing can be a very convenient way to meet people — admittedly, acquiring language from someone from the U.S. is not seen as prestigious as acquiring language from someone in the U.K. — and you should go out of your way to socialize as much as possible with the locals.
I wouldn't count on finding the guy of your dreams who happens to be 6'3 or taller, urbane and educated, and enchanted with you even when your hair is dirty and you're wearing torn jeans and a T-shirt with writing on it and no bra. However, one never knows. Que sera, sera.