re: trains - there are none between the cities. Best bet is to fly WestJet. Not entirely sure on the cost of the flight...I would think it would be slightly less than $200CDN.
Hotels close to the 'dome - it depends on your price range. The nicest are either the Hyatt Downtown or the Sheraton Eau Claire - both are downtown and are close to the c-train line (only a couple of stops between them and the 'dome...$2.25/trip)...I think there's a Holiday Inn in the area & some other chains but those won't be quite as nice...someone who's stayed there might be able to give you better advice
Enjoy the trip!