Ernesto's 1521 Cafe (1521 Spruce) is very close to the theater. It's a small place (in the cozy sense, not in the really loud and annoying sense) with good Italian food (and amazing Tiramisu!) http://www.ernestos1521.com/
A few come to mind. Estia has a nice three course pre theatre meal. Amis wouldnt be that far, and you should be able to get a table around 5pm. Zavino wouldnt be that far either and has a nice selection of pastas and pizzas.