Focusing on Hampstead proper, the first question you have to answer is whether you want a school that will go all the way through A-levels and therefore avoid the 11/13+ process or if you want to focus on a prep school which then might unlock a wider range of choices for your children when they are pre-teens?
If you want schools that go all the way through you would be looking at South Hampstead High School for Girls and UCS for boys. Both are good schools (#34 and #52 in the country based on A-level results), however, this is a part of the world in which there are parents for whom the sun rises and sets on Westminster, Saint Paul's Girls, Eton etc. and those two would not be seen as “good enough.”
The other main option is to focus on prep schools.
For boys, you have
The Hall: Selective and high-pressure/competitive environment (posts on this site refer to it as “fierce”).Lots of boys to St. Paul’s, Westminster and Eton.
St. Anthony’s: Catholic/faith-friendly, non-selective, but academic. Good pastoral care. Top boys to Highgate, Westminster, Eton, and City of London but student body has a broader range of abilities so lots to UCS and Merchant Taylors too.
Hereward House: Don’t know much about this school, except that sports provision may not be the best. Leavers profile similar to St. Anthony’s: City of London, UCS, Highgate, Westminster.
Girls (I only have boys, but based on experiences of friends)
St. Christopher’s: High-achieving, academically selective school. Top girls to City of London Girls, Highgate, Godolphin and Latymer as well as South Hampstead.
St. Mary’s: Catholic/faith-friendly, non-selective. I know people who have their daughters there and are very happy. The school is friendly and suits both quiet and boisterous girls. Destination results not at the same level as St. Christoher’s across the board if that sort of thing matters, but keep in mind the role that academic selectivity and a culture of tutoring play in generating results.