Re: Cost of private Arabic classes?
I'd also suggest looking into training facilities first. If learning at home is a preference, then for a universtiy professor... $60/hr sounds o.k. - I would have expected something around $50/hr.
What type of courses does he teach at the university? I've taken a course at the university myself and it was a gora professor who did an impressive job in teaching students who didn't even have basic knowledge of the alphabet. You're probably going to be much better than that so the task won't be as daunting... may be you can emphasize this in your "negotiation".