Below are the suggestions that I provided, in case other people are in the same boat and should stumble across this. (Below that are links to other self-guided walking tours for those with more time or mobility.)
I do want to give a tut-tut to some of the tourist groups out there, including the Exchange District Biz and Tourisme Riel. They tout their walking tours, including self-guided versions using their brochures, but don't put digitized copies of these brochures online. This makes it a difficult for people with limited time, or who want to set their itineraries before they come, or who are visiting outside of business hours, to access them.
Here are my suggestions with links to the guides. Note that I was keeping their 2 hour limit in mind !
Union Station: As you disembark, check out the station that you are in, which is a National Historic Site ! It recently celebrated 100 years and this nifty video was commissioned by Via Rail to commemorate it.
Broadway: Broadway is the street that runs into the Via Station, very easy to walk in that amount of time. The Winnipeg Architecture Foundation has a self-guided tour called Broadway Modern, which looks at post-modern architecture along the street. You can download a free copy of the booklet here.
If you walk up Broadway about 15 minutes, you will find the Manitoba Legislature Buildings and grounds. Here is a self guided tour booklet. You can also walk into the building and they'll let you check out the main public area which is pretty impressive.
You’ll also find coffee shops, food carts etc. along Broadway if you want a snack under the trees before you get on the train again.
The Exchange District is about a 15 minutes walk away. If you head north from the train station, you get to Portage and Main. Anywhere north of that point is the Exchange District, a National Historic District.
If you cross Portage and Main, which in itself is a bit of a trick - better to stay above ground than use the concourse - go to the east side of Main Street, between Portage and City Hall. Just behind that side of Main is really the heart of the district with many of the old refurbished buildings, Old Market Square Park etc.
This is a link to an older pamphlet of a self-guided walking tour. There is a newer version which the Travel Manitoba Centre at the Forks will have in their pamphlet rack. I can’t seem to find an online version but will keep looking !
The Forks National Historic Site: "The Forks"is the top tourist destination in the city and right behind the train station. Here's a site plan.
This is a walk through the Parks Canada portion of the site, but does not seem to be in booklet format. Again, the biggest Travel Manitoba bureau is right there so you'd be able to get a ton of publications and maps of the site there. Unlike other parts of the city, the Forks is signed well to help wayfind historic sites and points of interest.
The building with the tall spire under construction is the Canadian Museum for Human Rights, which will open in the fall. Next to that is the also spired Esplanade Riel bridge.
St. Boniface: Across the Esplanade Riel is St. Boniface, the location of the city's original French settlement.
Facing the river is the facade of old St.Boniface Cathedral, the modern church is build behind it. Out front of the cathedral is a cemetery where many prominent Franco-Manitoban leaders are buried, it includes the final resting place of Louis Riel. I can't find any online versions of the tourism brochures for that part of town, but here's a video about the cathedral and its grounds.
That should give you a pretty good range of activities in that two hour slot !
Fort Rouge Walking Tour
Louis Riel Walking Tour
Museums of Manitoba Road Trips
North Main Walking Tour: From William to Higgins Avenues
Routes on the Red: Numerous self-guided tours by foot, bike, boat and ski ! They include maps, pdf pdf printouts and time estimates.
St. John's Cemetery
Winnipeg Architecture Foundation offers a number of tour booklets. They are available for purchase in a nice pocket-size version. Some, like the Terra Cotta Tour, can also be downloaded free of charge.
Here's a link to a number of GPS tours of the city. The "light version" of the app is free.
The Winnipeg Architecture Foundation has outfitted a number of buildings with QR codes that you can scan with your smart phone.