Darwin had better be careful: if places like this keep appearing, it'll lose its reputation for gruff, frontier 'charm'. Lucky Bat would be at home in Melbourne's Fitzroy, with an arty atmosphere, orange blossom sodas and all manner of exotic teas. The food has the lightest touch (spanakopita, baba ganoush...), while the back courtyard has a lively, intimate feel.
Combine it with a morning at Nightcliff Market.