Harrow's nappy valley is West Harrow. All the roads around St Peter's Church on Colbeck Road - lots and lots of families with young children. Lots of baby stuff at the Church and Doctors Surgery within it. Very friendly and well appointed local park. Walkable to Harrow on the Hill where there are some nice cafes, pubs and restaurants.
Harrow on the Hill is very nice indeed - doesn't look like the rest of Harrow, more like Richmond or something - but the housing stock is incredibly limited and massively overpriced IMO. Roads leading up to it like Roxborough Park and Whitehall Avenue are very nice.
I live in the County Roads (stretch along the Pinner Road when you look on a map) which are always listed as 'desirable' (closer to main tube station on the whole) and again, quite a lot of young families, but I think West Harrow is a better bet personally (we didn't know the area either when we moved here - I would have gone to West Harrow had I known). The houses in the County Roads are a bit bigger than those on most roads in West Harrow I think.
Avoid anything around the Kenton side of Harrow I would say. Sorry. And well clear of South Harrow. Sorry again.
Roads directly around Radnor Avenue etc are nice, to the north of the main town centre. As you get over to the Sheepcote road side of that set of housing, it seems to go downhill a bit.
Pinner is good for cafes etc. If we stay in this area long term, we would likely move to Pinner.
Harrow town centre is not very nice - more functional than anything else.
There is plenty for kids in and around Harrow, definitely. And it's an easy run out to proper countryside too.