Hi, Joni, and welcome to the forum. It's a shame that Doll's and Burger's have both closed, as those offered two very good answers to your question. To my mind, this makes it all the more important that we support our remaining local good-food shops. I try to give Lotsa Pasta and Rainbow Blossom a lot of business, because they're local and good. I won't deny that I sometimes to to Whole Foods and Trader Joe's, but I try to spend $2 at Lotsa and Rainbow for every $1 that I spend there.
Choi's, as you mention, is worthy, and there are tons of other small ethnic shops around. Some I identify more by location than by name. The Russian/Internationa/Bosnian shops on Old Bardstown Road in Buechel, and a Chinese/Asian shop nearby. The Chinese place at the corner of Preston and Gilmore Lane is excellent, and the big Asian/Vietnamese grocery on the west side of Preston near the railway crossing is excellent, too. Lots of little Latino bodegas and panaderias around ... quite a few on Preston and on Northern Boulevard in Clarksville; a nice one on La Grange Road near Hurstbourne. There's a little strip mall on the south side of Westport about a mile west of Goose Creek with both a Middle Eastern grocery (Nara's, excellent) and a taqueria/bodega. Al Watan on Klondike Lane for Middle Eastern dining and grocery. A very good Indian grocery adjacent to Shalimar, SW quadrant of I-64 at Hurstbourne, near Liquor Barn.
There's tons more, but that's my personal quick brain dump.