Experiences like Sugiyama
Rosanjin and Kyo Ya are the two other Kaiseki places that I am familiar with in NYC. I have never been to either, but hopefully someone else can comment.
Degustation serves french/spanish tapas, but it certainly fits your description of a small place where the experience is personal, especially if you interact w/ the waitress and chefs.
Edit to include: Graffiti, a really small and personal indian style small plates place in the east village.