The restaurants in what could be called the East Village’s Little Tokyo typically stick to modest grub (ramen, yakitori, and other fun food sold in izakayas). Kyo Ya, however, offers a glimpse of kaiseki, the intricate Japanese meal originally served during a formal Japanese tea ceremony. Even if you don’t spring for the tasting menu — which requires at least a day’s notice — you can try plenty of the cuisine’s complex and occasionally esoteric dishes here à la carte. Delicate monkfish liver, often described as “foie gras of the sea,” lies in an umami-rich dashi-based sauce; sweet, faintly peppery grated daikon brightens the liver’s richness. An order of bozushi (a type of pressed sushi) presents rectangles of tangy rice, each topped by a sweet, buttery slice of marinated mackerel. The setting — an elegant union of handsome woods, soft lighting, and minimalist flora — echoes the meticulous arrangement of the food. Still, the neighborhood and the young crowd make Kyo Ya feel more easygoing than formal.