One great day trip from Edmonton is to Elk Island National Park.  Drive east on the Yellowhead Highway (Highway 16) for about 45 mins to reach the park.  There are lots of walking trails here ranging from 2 km to 20 km.  There are open picnic areas and group picnic shelters with (wood-burning) stoves for cooking in a number of locations through the park, with a larger number in the main area adjacent the lake.  Overnight camping is permitted in designated campsites.  Golfers will delight in the golf course adjacent to the campground  and main day-use area.

Elk Island is home to a herd of buffalo (bison) which you can often see right from the highway. Do not approach the buffalo! Although they may appear tame, they have injured visitors who have gotten too close. It is also common to see deer, elk, beaver, lots of birds, and sometimes moose (called "elk" in Europe) -  moose are less common.  The park is open year round, but is less accessible in winter months.

Between late May and early October, you may combine your trip to Elk Island National Park with a visit to the Ukrainian Cultural Heritage Village, located on Highway 16 just east of the national park's boundary. The Prairie Provinces had a large wave of Ukrainian immigrants between 1892 and 1930, and many Canadians are their descendants. This living history village collects a number of historic buildings related to the Ukrainian influx, which often reflect traditional Ukrainian construction styles. Costumed interpreters help to show what life was like for these people as they tried to establish themselves in their new prairie home. Virtual tour (available in English and Ukrainian). 360 ° virtual tour in QuickTime

Sylvan Lake is about an hour and a half drive south on the Queen Elizabeth II Highway (QE2).  There is a beautiful lake and beach here as well as waterslides.  The beach is popular with both locals and tourists; so, it can get quite busy. There are both motels and camping in the immediate area. 

Although it may seem possible to make a day trip from Edmonton to Calgary, the one-way driving time between the two cities is three hours, making for six hours of driving in total. If you're still interested, check Inside Calgary: Museums and Attractions on TripAdvisor.