You don't necessarily need a geared bike for a bad knee, and I honestly think the "fixed bad for knees" argument belongs with the brakes vs. brakeless crowd, even though Don's suggestion towards a geared bike had some good points.

I broke my tibia and ruined my ACL and PCL back in November. All I did was drop from a 49t to a 42, worked to a 44, now back to a 49 since yesterday actually. My knee feels pretty awesome and my right leg is nearly 100% in terms of muscle mass. I don't have full extension just yet, but that's a scar tissue issue that's getting resolved on Friday with the scope. My knee feels great no matter what I do on a brakeless fixed though...