June: Glacier National Park, Montana
If you want to head somewhere with "glacier" in the name, summer is the best time to go to Glacier National Park. Of course, the park is beautiful in the winter. But clear skies and gorgeous temperatures in the low 70s really illuminate the crystal waters and mountain peaks of the Crown of the Continent.
U.S. News and World Report notes that June lodging rates are the lowest of the summer. With chalets and resorts hovering at around $160 or below, it's not wrong.