CSS: height- fill out rest of div?

If you know the exact height of #widget (100px in your case), you can avoid using JavaScript by using absolute positioning:

#sidebar
{
height: 100%;
width: ...;
position: relative;
}

.widget
{
height: 100px;
}

#rest
{
position: absolute;
left: 0;
width: 100%;
top: 200px;
bottom: 0;
}