Those three are all large residence halls and the houses within them will differ somewhat, but if one were to make broad generalizations, BJ and Snitchcock (short for the two halls) generally have pretty good house culture from what I’ve heard. South, on the other hand, has had difficulties developing strong house culture and is a party dorm relative to the others (not that the two are exactly mutually exclusive, but the correlation certainly exists.) Halperin house in South is the exception to the culture thing, though. However, you can only select residence halls, not houses.
Both East and West are referred to collectively as South, at least among those of us not living there. People tend to just ask what dorm and what house they’re in, and I could only imagine the words “east” and “west” being used to describe physical buildings in this context rather than “where I live.” Note that no one actually calls anything Granville-Grossman; it’s all South, including the dining hall (which is Arley D. Cathey, who has a million things named after him anyway).
As a disclaimer, I’m someone who thinks a 15-minute power walk is a “pretty reasonable” distance since I live on the far east edge of campus, but learning to walk quickly is a useful skill when you want to sleep in 10 extra minutes and also helps you enjoy Hyde Park to the max. There are tons of good eats around the area, and I encourage you to walk (safely) and enjoy the neighborhood on the way to dinner rather than taking shuttles all the time. You can also save some money from delivery if you walk yourself 
Anyway, strictly in terms of location, you’re going to want to pick either Snell-Hitchcock, Max Palevsky (referred to as Max or MaxP) or possibly North (which will be opening next year). Snitchcock is literally right on the quad and they get their own cute little quad too; MaxP is right next to the Regenstein library/“Reg” and the Bartlett dining commons (although Bartlett food legitimately is worse than South food) and is hardly a block away from the quad. North will be a couple blocks north of the quad and further than the other two, but is, well, farthest north and will at least get you closer access to neighborhood restaurants and the like.
If you also want to be closer to the grocery store and local restaurants (there are some good ones), North and I-House are probably the closest to the good stuff up on 57th, 55th and 53rd, as well as the Treasure Island and Harper grocery stores. Stony Island is also up in the middle of the neighborhood and is apartment-style living. Snitchcock and MaxP aren’t horribly far off, though, if you don’t mind the aforementioned walk.
Now, in terms of convenience, which I’m going to say includes proximity to good study spaces and dining halls and the like, almost everything is honestly pretty great, in my opinion. Max is right next to the Reg and Bartlett; Snitchcock is on the quad anyway and is also fairly close to Bartlett; North is going to have its own dining hall; BJ and South have, well, South for food, the law library and arts center isn’t far and offer good study spaces and events; I-House is going to have some weird new meal plan, but it’s a big pretty building with lots of study space and lots of speakers and events happening weekly. There’s a convenience store in Bartlett, South, and I-House, and I believe there are going to be stores in North as well. Stony Island is the only remaining dorm that is fairly far, but there have been further (cough cough don’t get me started on the satellites cough cough) and they have balconies and apartment spaces, anyway.
There are good study spaces everywhere, really. Also check out the food trucks on campus that show up every weekday for lunch, I’d love to give pointers on those
And no problem! Happy to help 
Hope this wasn’t too long-winded lol.