Manhattan is the most density-rich market in the US. Nearly every address has groceries, transit, parks, and restaurants within a 5-minute walk. Differentiation comes from which subway lines you're near and how quiet (or not) the block is.
The West Village, Greenwich Village, Murray Hill, the Upper West Side west of Broadway, and the residential blocks of the Upper East Side tend to be quieter than the avenues and tourist corridors.
Midtown West, Union Square, and the Financial District sit on the most subway lines. The Upper West Side (1/2/3 + B/C) and Upper East Side (4/5/6 + Q) are well-served too.
Central Park dominates the middle of the island. The Hudson River Greenway runs the entire west side. The High Line covers Chelsea. Riverside Park covers the Upper West Side. Tompkins Square and Washington Square anchor the East and West Villages.