Gee, what do you mean by "best" and "bistro?" Are you looking for food, atmosphere, people, noise, decor, price... ?
If you want atmosphere, good food, and NOISE NOISE NOISE

by all means try for Balthazar or Pastis. I like them, but only before the crowds show up.
One of my neighborhood favorites (although it too gets noisy as the evening goes on) is Le Zinc, on Duane Street in Tribeca. It's a reasonably-priced offshoot of the **** Chanterelle, with a wide range of kinds of food (from a dynamite bacon-cheese-burger, to sauteed skate wings with brown butter & capers to steak au poivre -- classic bistro food) and a terrific wine list (would you believe a $16 bottle of Syrah from Baja California?). It's also kid-friendly. However, they don't take reservations, so after 7PM you usually have to wait. (If you want an idea of some of the food they serve, look at David Waltuck's "Staffmeals from Chanterelle.) If I didn't love to cook so much, I'd eat here every day.
Also, for casual and inexpensive, I love Franklin Station, a Malaysian-French bistro also in Tribeca. Simple French salads and sandwiches, and SPICY Malaysian noodles and other dishes.
Hey, you should ask Kyle what places he likes!