You'll be stuck downtown, so forget about low priced places. With that said...
1) Biodome, Planetarium, Olympic Stadium, Botanical Garden and Insectarium for all your nerdy needs. They are all conveniently situated close together in the eastern part of town. It's a short subway ride from downtown (go out at Pie-IX station). That could easily fill your entire Sunday.
2) Old Port is great if you get a nice day or evening to walk around. 'Muricans like the "European" atmosphere of the place. You can rent a bicycle for some nice cycling all over town (the bixie system). While there, you can check out the "Pointe-a-Calliere" historic museum.
3) For drinking, you most try some of the micro-breweries from Quebec.
4) For smoked meat, the classic place downtown is Reuben's Deli. It's expensive, but a good smoked meat. For Poutine, just go to any "La Belle Province" or local fast food place that is full.
5) St-Denis, Crescent and St-Laurent street are all buzzing street with a lot of action on a nice evening. Crescent has a nice Irish Pub that has live music.
6) Montreal has the largest underground city in the world. You could explore that.
7) Forget about skying. Mt Tremblant is almost 2 hours away, and by the end of April, the conditions are crappy.
8) If you need a nature break, you could go climb Mont-Royal, for a nice view of the city.
Like Protege2886 says, don't be afraid to speak english. Most people in Montreal speak it especially if you stay in the touristic and downtown areas.