In New Orleans, a neighborhood restaurant is often worth a trip across town. It’s the funky joint that gets glossy press and attracts swarms of tourists, who imagine themselves to be modern-day Christopher Columbuses discovering unknown lands of gumbo and fried seafood. In other towns, a neighborhood restaurant is mainly a place to eat.

La Vita, a new Italian place in Mid-City, is closer to how the rest of the country defines a neighborhood restaurant. It’s casual enough that you can walk ...