Once you have your own equipment, a number of locations are open to X-country skiing. In addition to local sites (link) and the aforementioned Lake County parks with ski rentals, there are a number of parks with suitable trails. In Indiana, snowmobile trails are off limits to X-country skiers. Trails in Salamonie SRA may cross the snowmobile trail. Choosing trails which do not cross is advisable.
Within 1.5 hours:
Tippecanoe River State Park (link). Gentle rolling trails for the most part, suitable for beginners.
Buckley Homestead County Park (link). Old farm with rolling hills, suitable for advanced beginner.
Bluhm County Park (link). Check the property map as part of this park is hiker only. There are lots of multipurpose trails which do allow X-country skiing. Suitable for beginners.
Within 2.5 hours:
Calumet Trail (link). This trail runs along the South Shore and is suitable for beginners and distance skiers.
Indiana Dunes National Lakeshore (link). Although several areas have trails one facility (link) doubles as horse trails in the warm months and ski trails in the winter. At one time, this was known as Lo-Co-Ki-We but is now known as Glenwood Dunes. Suitable for advanced beginners.
Lake County Parks (link).
LaPorte County Parks (link).
For more information about X-country skiing in Indiana, check out this great website for tips and locations of trails (link).