I use Mappoint, which despite being run by Microsoft is pretty decent. It doesn't have the "avoid highways" option, but you can choose "quickest route" or "shortest route", and the latter generally avoids most highways.
I've been toying with the idea of writing a bike-focused map site. Route-finding is not a terribly difficult problem, and the basic data is freely available. The tricky part would be identifying "bike-friendly" roads.
Last edited by elbows; 10-22-04 at 10:48 AM.