Rocky Mountain National Park is the obvious day trip from Boulder — about 75km north on US-36 through Estes Park, the park's gateway town. The park has over 350 miles of trails, 14,000-foot peaks, and spectacular wildlife including elk and bighorn sheep. Trail Ridge Road, which crosses the Continental Divide at 12,183 feet, is one of the highest paved roads in the United States and open roughly June through October.
Estes Park itself makes a good stop for lunch on the way to or from the national park. The Stanley Hotel — inspiration for Stephen King's The Shining — is there and offers tours.
For skiing, the resorts of Eldora Mountain (45 minutes west), Breckenridge, and Keystone are all within day-trip distance from Boulder.