Maligne Canyon is almost a must. What a cool place. Take the time and go there for sure. Bring a snack, good footwear and go down the trail a bit. Pretend you are going to Jasper park lodge. Instead of going right to the lodge go left about 10 - 20 minutes up the road is Maligne Canyon.
Near Jasper Park Lodge is Edith lake and ???? (carvelle?) Lake. Both are nice and again good light hiking trails. Jasper Park lodge is right there and worth a look. Some trails here to wander on as well. Possibly skating on the lake there too.
Find the aquatic center. there is a road that goes up a big hill. Take that road it leads to another great lake and some great scenery.
Aquatic center is okay. New boilers, steamer and mechanical have turned this place around. Tub is usually pretty warm. Steam room is nice. Pool is basic and water slides for kids.
There is a Gondola but I do not beleive it runs in the winter.
If the roads are good, fill your tank and head down the Banff Jasper Hwy for an hour or so. Or drive right to the Columbia Ice feilds. there is a huge lodge etc there for lunch. Further on is Saskatchewan crossing (GET GAS) with a hotel and restaurants etc... about 2.5 hrs from Jasper to Sask Crossing on good roads. Don't forget gas ! Did I mention gas ? Don't ask.
As you take the road to Marmot you will come to a intersection that you would go right to go to Marmot. There is a road that goes straight. IF you have a 4 X 4 or if the roads are good take that road for 1/2 hr or so (It might be closed during the winter, if so I would stay off it's pretty remote back in there), very nice out of the way drive. If you stay on that road about 1hr you end up right at Athabasca Falls. I have only seen it in the summer but I would think winter is equally fantastic.
Almost all the way up to Marmot is a parking lot that alot of people go X coutry sking here. There is a ice fall canyon in there somewhere as well, but I have never been. I think there are tours you can take. Supposed to be pretty nice probably worth the effort.
Drinking. THe "Atha B" (Athabasca Hotel) Whistle Stop Pub (right across the street)
The high street is pretty cool but hit it early afternoon as Jasper closes up most shops early in the winter. Don't count on alot being open late.
on the main street right by the train station is a bistro. They make the best damn foccia sandwich in there and lots of good home made food. I can never remember the name.
L & W Restaurant is a good economical meal and good value.
Lots of pubs and coffee shops and candy shops.
Used to be a place called OOPS and SCOOPS for ice cream sundeas etc....
As said by others Jasper is a quiet little mountain town with a nice ski hill. I hope it never changes.
Banff is nice but those crowds I can do without.