I don't claim to be a coffee expert (that's Andy). I started liking coffee a couple years ago, and can't believe I went that long without the cappuccino in my life. One of the coolest coffee shops is the Roasting Plant Coffee Company (and I now live close to the West Village location), started by a former Starbucks exec. The coffee is sent through the "Roasting Plant Javabot," which roasts raw beans, grinds them, and brews the coffee WHEN IT IS ORDERED. It is definitely the smoothest, and almost creamy, cup of coffee I've ever had. There's also room to hang out, a rarity in New York coffee shops.
Serious Eats gave Roasting Plant a seriously coveted award when they named their chocolate chip cookie the best in the city.