Of course Manhattan has incredible restaurants, but I'd rather sink my teeth into Brooklyn any day. With all the choices "the city" offers, I think people tend to go with what's comfortable and choose a few favorites over and over and over again. My parents talked of two: "21" (not the 21 Club, mind you, but Hop Kee, a basement den with fluorescent lights at 21 Mott Street in Chinatown) and Viand, the pint sized diner where they ate amazing bagels with cream cheese and jelly near their apartment on East 63rd Street.
I lived on the Upper East Side when I first moved to New York in 2000. I go up there now and all culinary memories of my two years there disappear. There was a dirt cheap dumpling shop (don't remember the name) and a few chains, but everything else is a blur. Next came the East Village and all that comes to mind is the meaty borsht from Veselka, pizza from Two Boots and goat cheese salad from 7A (all of which have very good food and very limited ambiance). There are thousands of cute places in that neighborhood - many relatively new - but somehow I never bothered to pop in.
But then I moved to Williamsburg, the neighborhood where everyone's a waif and you can eat yourself into a local food coma. Porter and I rotate ourselves through these joints and love them all dearly. Click on the eating/drinking sidebar for more info about these places. They're really so, so good. (And I pray that someone can read that itty bitty map - it took ages to create). Note, I have omitted Egg (on purpose). It's delicious and cute, but all the great reviews have made the lines ridiculous. You don't come to Brooklyn to stand around.