JJ,
I've been in South Bend off and on for about 20 years and have played pretty much anything and everything within 2 hours. Recommendations will depend on how much traveling you truly wish to do.
As has been mentioned, Grand Rapids in April is a crap shoot. If you decide to head that way, downtown GR is 2 hours. Southwest of Grand Rapids is Diamond Springs and on south side of downtown GR is The Mines. Tullymore or Pilgrim's Run north of GR will be 2 1/2 hours.
Near Benton Harbor/New Buffalo area, about an hour from South Bend, Lost Dunes, Dunes Club, Point O' Woods and Harbor Shores would be enjoyable. Dunes is walking only. All except Harbor Shores are private and all will be pricey. Just north of there before South Haven is Hawkshead.
Angel's Crossing an hour away in Vicksburg would be good. Very cool set of greens for a modern course, the idea for each borrowed from well known courses in England/Scotland.
If heading toward Indy, a stop at Rock Hollow is a must. Drive time is a little over an hour.
Others have suggested some healthy drives. If you head toward Purdue to play Kampen, plan a stop at Harrison Hills in Attica. From South Bend, it's a solid two hour drive to Kampen. Attica is another 35 minutes west of there. You could also continue down I-65 and stop in to Trophy Club in Lebanon with all of Indy just south of there.
French Lick is a 5 hour drive. There's just no good way to get there from here.
Don't turn away from some great options around the South Bend area. Warren is a given but I would also recommend in order South Bend Country Club, Elcona Country Club, Blackthorn Golf Course, Hampshire Golf Course and Erskine Golf Course.
PM me if you have any questions.
Ken