I agree with Omotesando and I would add Marunouchi, but they won't have a real neighborhood feel.

I've seen some cafes near the Andaz hotel, on the street that seems to go in the direction of Tokyo Bay and is tree lined with a block or two of businesses in mostly low buildings and at least one wall mural; I think there's a bicycle repair shop too. The place I'm thinking of is across the street at the redlight from the Andaz. I've noticed a couple places with outdoor sidewalk tables that look pleasant. There's also at least one cafe in the big Toronomon (spelling?) Hills building that contains the Andaz, on the street level and also on about the second or third floor,