The premier golf course around
Also a fun golf choice
There are polo games that can be watched either Saturday or Sunday.
This is 10 minutes outside Dayton and can be made as long of a Hike as you want
This is about an hour to an hour and a half drive to the top of the mountain. The hike itself is moderately strenuous and takes about 1.5 hrs round trip.
A historical mansion in Sheridan.
This is a driving tour of the early coal mining around Sheridan
There is fun stream fishing available in the Big Horn Mountains. You will need a WY fishing license.