Pick two neighbourhoods a day and stop trying to do the rest.
This is a shape, not a schedule. Each day has two anchors and a lot of slack, because 3-day itineraries that book four things a day fall apart the first time lunch runs long. Move things around freely — the neighbourhoods are grouped so that walking between stops actually works.
New York is where budget mismatches hurt most: a $95 tasting menu and a $4 slice are both authentic experiences. Agree in advance which meals are group splurges and leave the rest optional so nobody's quietly overspending.