1. Edge of the World
The "edge of the world" is a short walk from the Marmot Basin road. There's no parking so you'll need to just park on the side of the road, just past the last bend before the Marmot Gates. It's a great spot to catch sunset or a nice view overlooking Jasper.
2. Whistlers Mountain
Whistlers towers over the town of Jasper, but the doesn't mean that this hike is extremely challenging. Once you clear the treeline you're greeted with some phenomenal views - the best part though is that you're only halfway there. The entire trail is well marked and is a real treat to hike.
It's 6.8 km in distance and can take anywhere from 3-6 hours. It look myself and a few friends just shy of 3 hours to complete the hike, with a few photo ops along the way of course. You can find more info on hiking Whisters from the good folks over at Hike Jasper here.
3. Pyramid Lake
Just a quick 15 minute drive from town, Pyramid Lake is named after quite possibly the most recognizable mountain in Jasper for its pyramid-like shape. There a loads of activities to do at the Pyramid Resort, everything from water activities, grub and your accommodation needs.
You can also access the Pyramid Lake and Athabasca Overlook trailheads here. Both are short hikes (1.5 - 2.5km / 2 hours) and offer great views of the valley.