There is no motel in Brodhead but there are several small B&Bs and private rentals.

Little Vintage Charmer Cottage Mention EAA Chapter 431 for a discount
Go-Inn Home B&B 608-897-8138
The Pines – Albany, Wis. 608-558-0179
AirBnB local area rentals, including Earth Rider Hotel downtown.
Crazy Horse Campground (approx. 4 miles from airport) 608-897-2207

MOTELS AVAILABLE IN MONROE, WI (12 miles west):
AmericInn (608) 328-3444
Super 8 (608) 325-1500
Gasthaus (608) 328-8395

More lodging is available in Janesville and Beloit, both about 30 minutes east.