Enjoy the sights and scenery of Jasper National Park.

Take the tramway to the top of the mountain.  On a clear day the view is spectacular.

If you enjoy hot springs, visit Miette Hot Springs.

Maligne Canyon is very scenic. 

Ditto what gecko said. Have lunch or dinner at the Jasper Park Lodge. Walk the Maligne Canyon. Ask the locals where good hikes are. We stayed in "Approved Housing" (I think that is what they are called. B&B's without the breakfast) which are much cheaper and very nice. Most importantly, enjoy yourself. Jasper is amazing. You might want to take the drive to Banff and see the ice fields along the way, but Jasper is worth a visit on its own.

Ditto both the above and if you drive to Banff - best drive in the country IMO - take the first 80 kms quickly except for a stop at Athabasca Falls because the most stunning parts IMO are from about there on (I'd guess it's obvious that you'll likely need time before or after your 27 hours, but well worth it if you can).  And if you can't but wou7ld like to see what it's like, about 65% of shots here - http://intersiteimaging.com/Top/Mountains/ - are between the N. edge of the Columbia Icefield and Banff.  Ano0ther 20-25% are within an hour off that highway but all are from the road.

If time doesn't permit that, there's a helo tour that runs from about 20 kms east of Jasper over the mountains.  Expensive but worth it on a crystal clear late afternoon.  About 50% of these older backcountry shots - http://intersiteimaging.com/Kodachrome/Kc-Mountains/ - are typical of what you'll be flying over.  My $.02.

If you stop at Parks Canada building they have a sheet of easy day hikes

Take the cruise-sightseeing boat on Maligne Lake-to Spirit Island ( I've never done that-we canoe to  the end of the lake but you have limited time and it's a great view

Eat at the Bakery called The Bear's Paw-oops I think you might be gluten free....

Raft the River-they have sedate tours that I did while Pregnant but also more sedate ones for and also wilder ones-see what's available while you are there. Many are 1/2 day and they provide what you need ie wetsuit, pfd etc.

You'll need a car for Maligne and for Miette Hotsprings-lovely hike from Miette -UP and then soak after

Have done a trail ride from Jasper too.

At night time, drive to the local dump and watch the bears.

bring a camera (and not just your mental one); your pigs will love you even more for it :3

http://www.jaspernationalpark.com/

I've only been to Jasper once, and that was about 20 years ago. I remember taking the tram - it was incredible. My main piece of advice is to step off the beaten track and enjoy being surrounded by nature in the incredible Rocky Mountains. Be prepared to have your breath taken away - both literally and figuratively - especially if this is your first time in the Rockies! Like Inanna said, bring a camera and take millions of pictures! Around every corner you will find a scenic vista - each more beautiful than the last.

I was just there last September - lovely little town.  We stayed in a great little B&B suite.  Had planned a trip to Maligne Lake for the cruise noted above - but woke up to horrendous stormy weather ... the only nasty weather day of our whole 2 weeks in the mountains! - so we missed that.  There is a bus that goes from the centre of Jasper out to Maligne Lake for the cruise, if you don't have a car available. 

If you do have a car - it would be a feasible day-trip to drive down the Icefields Parkway as far as the Columbia Icefield, stopping at the various waterfalls along the way, which are very lovely.  The Icefield tour (dress warm!) is terrific, and worth the cost IMO.  And then drive back to Jasper - although the road is the same one the scenery will look quite different - different time of day, different light, different vantage point.  Enjoy!!

Willl you be travelling to other areas in the Rockies?  So gorgeous!!

P.S. - there is also a gondola in Jasper - so if you want, you can ride it up for some alpine vistas.  There may be some alpine hiking trails at the top - can't say, because we did not do that, but many places do have that option.  Alpine hiking is wonderful!!

Thank you everyone for your wonderful ideas!!! :)

I'm looking forward to our trip!

Today is our BIG day!  See you all in a week's time!  I'll respond to posts then :)

Thanks everyone! 

Exciting!  Bon voyage Sterton!!

Have fun Sterton!

Thanks Carolla & somegalfromcan!  The trip was excellent.  I loved the train but disliked the plane!

We did the tram trip and shopped & ate around town.  I loved how the huge waterslide at the indoor Aqua Complex was warm water.  I can totally see living there!  The Athabasca Hotel was excellent!  Great service!!!

I'm glad you had such a good trip Sterton!

Thanks somegalfromcan.  I would definitely do it again :)