There used to be a typical Gujarati restaurant, which actually used to be more of a 'mess' or canteen on the ground floor of the Gujarati Samaj near High Court/ Sowcarpet. There was authentic Gujju food being served there and in the traditional style in stainless steel thalis with 'vaatis' of dahi, dal etc, and hot garma garam rotlis spread with ghee. Its hard to locate that place though...tucked away in a small gully.
But that serves only vegetarian food. There's also Thali Corner at Windsor Palace, Balfour Road, Kilpauk. (Tel 26471100) and also Rajdhani Restaurant at Express Avenue Mall, White's Road, Royapettah. There are quite a few good non-veg joints...depends on your taste and the budget you are looking for.