Petite Abeille is a Belgian cafe chain around the city, and it's worth a visit.
I've been to the one in Tribeca several times and have an excellent experience every time. Waiters are very attentive, seem to know their food if you ask for a recommendation, and they have excellent daily specials - usually a fish with potatoes and vegetables so you'll eat hearty, and have sampled all the major food groups!
Every fish dish I have had here is excellent. Mussels are also great as is the salad nicoise, and the omelettes which change day-to-day.
In nice weather, outdoor seating is a must. Otherwise, inside is very bright and cheery - just make sure to arrive early for lunch as the place is usually full before 1pm during the week.