If you go up to Lake Louise, go really early in the morning or late in the day to avoid summer crowds (and not wait endlessly for a parking spot). And check out Johnson Lake near Banff on a hot day for a swim in a mountain lake. There's a small beach there too.
If possible, don't go to Banff in July or August as it's very busy. If you go off-season, you'll have cheaper prices, less crowds, and all the same great stuff. June or September is great.
When staying in Banff, be sure to drive the Icefields Parkway up to Jasper. It's absolutely breathtaking.
If you're in Banff, make sure to eat dinner at St. Jame's Gate. It's a "true" Irish pub. The food is delicious, the staff friendly and helpful, and the ambience very cozy. During the winter, this is THE place to get tips on the local ski areas, as most instructors, etc. stop in for a beer after work.
Banff National Park is somewhat indescribable; its beauty lies not only in its obvious scenery but runs through its crystal clear glacier river, howls within the surrounding towering mountains, and whispers along its beautifully untouched streets.
There are a few options for Banff hostels; you will be located either on the main strip (good for a winter stay) or around Tunnel Mountain. Visit the travel centre downtown to educate yourself on which trails or activities are currently offering what you're looking for! Banff's nightlife is always booming, with dance clubs near/on the main drag.
Banff's year-round activities are endless. In the summer, be sure to hit up the dollar store and grab yourself a dingy on which to float down the Bow Valley River! Must-do mountains include Tunnel Mountain, a short walk from the town (about twenty minutes), where you'll catch the picturesque ski town at a birds-eye view. Sulfur Mountain, which is a two-hour hike for the averagely fit, can pose a great challenge for runners; a short gondola ride to the top for the faint of heart is definitely worth the value and the energy you save to walk around the top of the mountain. For the more adventurous of hikers, Mount Rundle and Cascade Mountain are must-dos. Close to town, you can't skip the Fairmont Banff Springs castle in the mountains.
Winter is a whole different story; Banff is a snowboarder's or skier's haven. The town runs shuttles to three of their main ski hills periodically throughout the day on two main routes stopping at most Banff hostels and hotels. The three ski resorts include the closest Norquay ski hill, and the ever competing Lake Louise, and Sunshine Mountain; all are definitely worth a try. Lake Louise seems to be preferred by boarders due to its extensive terrain park. Sunshine is preferred by skiers due to its many rolling mountains. As for Norquay, it's a mere five minutes out of town and the only one of the three to offer night skiing.