My husband and I have a 20 and 22 year old, who have lived their entire lives to the age of 18 in the Los Altos Hills. So, I can share some true experience with you, as my husband and I have lived in the Hills for over 30 years and raised our family here.
The folks who live in the flats, have many opinions about the Hills, and their perceived sense that they are inconvenient. I do find that folks who are not used to my hill think it is MUCH longer than it actually is from town. Townies perceive distance differently (it feels farther to them) in the hills is my observation.
Most parents do not let their children walk in neighborhoods alone anymore, like we used to when I was a child. So, even if you live in closer in to town, you are likely to be supervising your children pretty closely. Another big change: Children's lives are scheduled. They no longer walk down the street and ring doorbells for a casual play date that is driven by the kids. Parents arrange these things. So, whether you live in the hills or in the flats, you probably are supervising your children pretty closely and driving them around to soccer etc quite a bit, not matter where you live.
I would say that in Junior High one of my children really did not like living in the Hills because unlike her friends who were sneaking out their windows at night, she was not able to do this, as "an animal might try and eat me!". You have more control over your pre-teens/pre-driving children when you live in the Hills.
I am never in a traffic jam on my way home, in the hills, but I have been in traffic on Grant Road near El Camino Hospital in the afternoon where it took 20 minutes to go two miles. This does not seem very convenient to me.
There are parts of the Hills that are more convenient than others. My home is 5 minutes from Hwy 280, and 8 minutes to the closest elementary school. You get much more value in terms of land, natural beauty and square footage in the Hills. The Hills are a very good value at this time. But you probably will have somewhat more driving time, and most parts of the hills are not walkable to town, although there is one section that is.