Frasca (already mentioned) is a good bet. Solid pizzas and salads, even some decent pastas.
Agave Bar & Grill is a non-Tapatio Mexican option. It's on Lincoln just south of Belmont. I've been there once and had a veggie mole dish that was good.
There's a whole series of bar/grilles around there (Belly's, Fizz, Bourbon) that each have some veggie options of varying quality.
Kite Mandarin & Sushi is on Lincoln just south of Roscoe. Decent sushi and other asian dishes.
Sapore di Napoli is on Belmont east of Ashland. It has thin-crust pizzas and pastas. The place is a more modest version of Frasca, and much smaller. It is also BYOB and there is a new and pretty good wine store on the same block called Wine Styles (terrible name).
Harmony Bar & Grill, which is attached to Schuba's, is at Southport and Belmont and has better food than most bar/grilles in the area. I recall there are several veggie options there but it has been more than a year since I've been there.