Does your friend want to go to a place that serves exclusively Vegetarian food or a place that also has good vegetarian food?
Totally vegetarian: Your choices are
Udupi and
Uru-Swati.
Mysore is not really authentic tasting.
Annapurna, Kamdar Plaza and Sukhadia are chaat places that also do dinner type food on the side.
Arya Bhavan always disappointed me whenever I tried that place.
Udupi is pretty good as they have South Indian, North Indian and Indo-Chinese vegetarian. I have never eaten the North Indian and the Indo-Chinese at Udupi as I always get their South Indian stuff, which is really good.
Uru-Swati has Chaat + South Indian + North Indian. Again, I have not tired the South Indian stuff at Uru-Swati as I usually get the chaat and North Indian stuff here, which is done well.
If you want to go to a regular restaurant that also serves Vegetarian; I like
Viceroy, Tiffin and
Nepal House. The Pakistani restaurants like
Khan, Sabri, Usmania etc are not vegetarian friendly, in that they have some vegetarian dishes but the restaurant does not put a whole lot of effort into it.
The art of living well and art of dying well are one. ---Epicurus