The easiest hike between Banff [1] and Lake Louise [2] is along Johnston Canyon, but there are also some more challenging options. The following three are my favorites.
Cory Pass (5.8 km/3.6 mi, 2.5 hours one-way) is a long, hard slog from the Fireside Picnic Area (the elevation gain is 920 m/3,020 ft), but once at the objective, a wild, windy, desolate area surrounded by jagged peaks, the view of dogtoothed Mount Louis is worth every bit of energy expended.
Rockbound Lake is a delightful little body of water tucked behind Castle Mountain. The trail (8.4 km/5.2 mi, 2.5 hours one-way) itself is unremarkable, but crowds are minimal and the lake is surrounded by impressive peaks. The trail begins at Castle Mountain Junction, 30 kilometers (18.6 miles) west of Banff.
From a signed parking lot along the TransCanada Highway three kilometers (1.9 miles) west of Sunshine Village Junction, the trail to Bourgeau Lake gains 730 meters (2,400 feet) over 7.6 kilometers (4.7 miles). Hikers are rewarded with the spectacle of a small subalpine lake nestled at the base of an impressive limestone amphitheater. Allow 2.5 hours each way.
Links:
[1] http://www.moon.com/destinations/canadian-rockies/banff-and-jasper-national-parks/town-banff
[2] http://www.moon.com/destinations/canadian-rockies/banff-and-jasper-national-parks/lake-louise-and-vicinity/lake-louise