Fron Chicago, take i57 to i80 west. Get off at exit #81 (rt 178). Drive about 3 miles south on 178 and follow the signs to the park. Starved Rock is 94 miles outside of Chicago.
Spring is definitely the best season due to greater water flow at the falls - if the waterfalls are your main consideration. The hike to the falls is easy (say, a 2 mile round-trip back to the lodge) and well-marked.