My mother and I have used Sony Cybershots over the past 10 years or so, upgrading every few years. I LOVE it because it's small, has a great zoom, great lens, great features (like hold the button and it takes multi pics, which is great for moving toddlers!) but my FAVORITE thing about this camera is how fast it starts up! In less than 3 seconds it's ready to go. And with kids, THAT is a must!
I have a D60 too, but that's for photo shoots (backyard, bluebonnets, etc.) over a travel, toss in your bag camera. It's great and I enjoy using it but it's big and hard to one hand.