There are no bars or cafes in Sterling, and none should be expected: this is conservative rural Utah, in a county that is predominantly Latter-day Saint. Alcohol is not part of the local culture, and the village has no commercial premises of any kind beyond what the park provides.
Bring your own coffee and anything else you need. Manti, 10km north, has a couple of small cafes and basic convenience stores. For anything resembling a broader selection, Provo or Salt Lake City are the nearest cities.