The town of Banff can be downright gaudy with all the tourist crap, but it also has it's charm. April might be the perfect time to go because it's not high tourist season. From Calgary it takes about 90 minutes to drive to Banff. The drive there is half the fun as the scenery through the foothills and then the approach to the mountains is wonderful. I suggest taking the alternate route (Highway 1A) as long as the weather is good. It's a smaller highway and your chances of seeing wildlife are greater.

Once you're there, it really depends on what you like to do. You can ride the gondola up sulphur mountain and the views from the top are spectacular. There's a nice restaurant up there too. You can hike to your hearts content, depending on the weather of course. Drive a bit further past Banff and visit Lake Louise. Or check out the Columbia Icefield. Banff hot springs. Skiing.

For something completely different and if you're into dinosaurs, you could head east out of Calgary to the badlands and check out the Royal Tyrrell museum in Drumheller.