I grow only one terrific variety of kohlrabi - Superschmelz. Superschmelz is a large Swiss heirloom variety of kohlrabi that can grow up to 10 lbs (I have only been able to get them up to 4 lbs). They are delicious eaten at any size and never get woody.
Store kohlrabi in a cool, dark place including the fridge or basement.
Peel the outer skin and remove any woody bottom stem that is still attached to the bulb.
Find kohlrabi recipes here.