Depending on your preference of hotels (basic holiday inn express or resort type) you should be able to find something. Walworth County is big on tourism and so has numerous lodgings (B&B's, hotels and resorts). I would suggest looking in Elkhorn or Delavan, but you will likely find more in Lake Geneva which are close by and only 20-25 minutes or so from Alpine Valley. I would try Grand Geneva Resort in Lake Geneva or google the area for other accomodations. Nearby cities to google are Elkhorn, Delavan (both are south of Alpin Valley). Cities between Milwaukee and East Troy are Mukwanago and New Berlin (probably not much to choose from there).
For something to do for half a day, take the mailboat ride on Geneva Lake. The main docks are in the heart of downtown Lake Geneva. Or, you can hike along the trail which circumnavigates Geneva Lake. The trail is along the shoreline and passes by numerous mansions.
BTW, who is playing at the Valley that day