There is the question as to whether Atwater Village is eastside or not - some might argue not or try to get lumped in with adjacent Silver Lake. Some might even argue it's in the Valley as Glendale - its northeastern neighbor - is.
I say: even though it's east of the river, it's not really Eastside, the same way that Silver Lake, Solano Canyon, Elysian Park, Los Feliz, and Griffith Park are not. Heck, Griffith Park used to (and technically still does) extend east of the LA River before the 5 was built. That's all part of the same community of "NoDo" North of Downtown (be it slightly northeast or slightly northwest).
Here is a "just ok" map of the communities in LA - it's not as detailed as I'd appreciate, but it'll have to do. (See how the Atwater delimma occurs?)
NoDo? Though it sounds like a prime spot for the next season of The Real World, I'll stick with the pirate analogies and keep Atwater Village in No Man's Land. For now.
Don't forget my humble proposal to split LA along Western Avenue. In 20 years, when enough westsiders have followed Brangelina to the eastside, you'll appreciate the foresight. Till then, appreciate the symmetry: