Not far from your proposed options is my fav "basic" Italian, Papa Milano at the corner of State and Oak. Great gnocchi, lasagna, pasta e fagiol and fagiol con escarole. Though it's only open until 11:30 weekends... below is a descrip from some restaurant site. There's a menu posted at amazon.com.
Papa Milano Restaurant
For over 50 years Papa Milano's has been feeding the patrons of Oak Street. This family owned restaurant serves the finest Italian cuisine, from veal parmigiana to pizza. People have been returning for over four generations to experience the warmth of the food and the friendly service.
Open: Mon. - Thurs. 11:30am - 10:30pm; Fri. 11:30am - 11:30pm;
Sat. Noon - 11:30pm; Sun. 1pm - 10:30pm
1 East Oak Street
312.787.3710