Hang in the cool dry if you have a place that is cool and dry. Lacking that, cut up and freeze. They still work perfectly stir fried or in any other recipe that calls for cooked onions.

Dicing up and freezing has become our preferred way. Freeze the cut up pieces spread out on a cookie sheet first, then put in freezer bags. That way they don't clump together, and its easy to grab a handful and put in soup or whatever.