I had all that when I was living in Westwood, which is far far far aaay from downtown, but I could have had that in belverly hills, or Culver City, or even (but just barely) Brentwood.
There is also a giant robot art gallery in sawtelle japan town, which I think is walkable, definitely bikeable.
my listed criteria wasn't even complete, just what came to mind in the 30 seconds i thought about it. there are plenty of neighborhoods that are walkable in LA (silverlake, hollywood, highland park, even north hollywood, etc.). the whole city doesn't need to be reachable by foot to be a walkable neighborhood.
sounds like your bar may be set particularly high or your assumptions about what you need to walk to may be extraordinary.
My definition would be could you live comfortably without ever using a car, such as being able to go grocery shopping without having to walk a ton, be near enough to the rail system such that you can get around easily, be in a neighborhood where going clothes shopping doesn't mean an inconvenient trip to a mall, ect.
i'll leave it to you to find the others, but one of my faves in culver city is the museum of jurassic technology (has a rooftop aviary): http://mjt.org/
> "My definition would be could you live comfortably without ever using a car"
that's a pretty high bar. how would you move in/out without a car/truck/van? carry everything by hand? i don't own a car but i use one periodically.
The majority of people who live in LA, live somewhere nestled into the bigger sprawl that is the region. While there are plenty of neighborhoods that have walkable aspects, the city is by no means walkable (even with transit) to huge portions of the city.