It seems obvious, but the best views of Manhattan are from outside Manhattan. Long Island City (LIC for short), which is located in Queens and situated on the edge of the East River, is one of the city's neighborhoods that gets to enjoy those stunning views.
This is a mixed use area: you'll still find industrial blocks with one or two trees clinging to life, but the neighborhood also hosts gleaming glass condos, vinyl-sided townhouses, and the Hunters Point Historic District, which features a number of beautiful brownstones built in the 1800s.
Families say LIC is a good midway point between the pace and density of city living and the quiet of the suburbs. It's also one hop into Midtown Manhattan which makes it an easy commute for anyone working there. It doesn't have the charm of other neighborhoods in the city but it does have some entertainment value: there is PS1, an old public school that is now an extension of the Museum of Modern Art, a giant skating rink, waterfront parks, and a kayak club.
And like any proper New York neighborhood, LIC has a good selection of restaurants and cuisines, ranging from affordable Mexican to upscale steakhouses.
Wall Street: 6.3 miles / 20-45 minutes by car / 40-45 minutes by transit
Rockefeller Center: 2.9 miles / 15-35 minutes by car / 20 minutes by transit
Jersey City: 10.8 miles / 35-80 minutes by car / 55-60 minutes by transit
Downtown Brooklyn: 5.1 miles / 20-40 minutes by car / 35-40 minutes by transit