This is heavily slanted towards Korean banchan right now. Please add yer favorites.
I've come to recognize that most K-town places have store-bought or shoddily-pickled banchan, and that very few places have serious pride in their banchan.
Favorite kimchee: Yongsusan.
Favorite kimchee at a regularly-priced place - the champagne-y, delightful stuff at Kobawoo. You can get a huge plate of it for $2 with the boiled pork belly dish.
It took me awhile to see and appreciate the fine kimchees -the ones that weren't just sweet/ferment/spice hit, but had that magical, bubbly-seeming, vinegary-champagney, delightful buzz.
Favorite pickled daikon: Jeon Ju. Unlike a lot of other pickled daikon, this really has an incrediblely intense, concentrated daikon flavor. This is radish, plus.
Favorite lightly pickled cucumber: Beverly Soontofu. (When I asked if they were for sale, the waitress gave me that grin that says, "No, that's how we get you here." It's a cross-cultural smile. I've seen it when a friend tried to negotiate the purchase of a gallon of aji at Mario's Peruvian.)
Favorite pickled soup: the radish-and-sprout-pickled cold soup at Sa Rit Gol, which has the same champagney ferment as the best kimchees, but more purely sparkling. This makes me weak. Still my overall favorite for banchan.
Favorite Armenian beet pickles: Sahag's, for savagery.
Favorite deli pickles: DAMN! What's that place on Sepulveda called? Johnnie's? I think it's Johnnie's. Er, their pastrami is little to me now, now that I know of Langer's, but this pickles still are a sweet, delectable marvel.
Otafuku, the Great Soba Joint, used to have truly stunning home-brined pickles, full of sweet, intensified life, but the LA county health dept forced a shut-down of all the home-brining Japanese-style pickling around the area. To my despair.
Favorite pickled carrots, Mexican style: El Gran Burrito. They just have great condiments all around. If you look carefully, there's sometimes a whole bulb of pickled garlic, which is almost more than my poor, weak heart can handle. Zippy!