October is the showpiece month in La Crosse. The bluffs turn color in early to mid-October, providing some of the best autumn foliage in Wisconsin, and Oktoberfest runs through the first weekend of the month. If you can only visit once, visit then.
Summer (June through August) is pleasant — warm, with festivals including Riverfest in July and steady activity on the riverfront. The humidity is real but not oppressive. Winter is cold and snowy, which matters if you are coming for outdoor activities: the ski area and the bluff trails for snowshoeing are genuine winter draws, but plan accordingly. Spring (April-May) brings flooding risk on the Mississippi, which is interesting to see but can close some riverside parks.