Ida has long been a favorite band of mine. In fact, Ida probably qualifies as "music for parents that kids will like too." When Elizabeth Mitchell became a mom (with Ida bandmate/husband Dan Littleton) they began to record some lovely records for children: You Are My Flower, You Are My Sunshine, You Are My Little Bird. There are many classic songs on these records that your child will recognize instantly. And better still, there are some inspired covers like "What Goes On" by the Velvet Underground! I can't recommend these records enough. They are filled with warm, acoustic arrangements and lovely harmonies. Elizabeth also recorded an album of children's music with Lisa Loeb called Catch the Moon.
Buy these albums:
You Are My Little Bird
You Are My Sunshine
You Are My Flower
Catch The Moon