Hotel blocks seem to not really be an option in Door County. Rob and I suggest you find a stay in Egg Harbor.
If you are flying there are a few options:
Green Bay Airport- 1 hour 15min drive to Egg Harbor
Milwaukee Airport- 2 hours 45min drive to Egg Harbor
Madison Airport- 3 hours 10min drive to Egg Harbor
Chicago O'Hare Airport- 3 hours 45min drive to Egg Harbor (We have personally flown into Chicago and made a fun drive out of it to Door County)
We highly recommend that you rent a car, but if that is not an option, this is the local taxi service since Uber and Lyft are far and few between.