Mont Ste-Anne near Quebec city has some of the best mountain biking in Canada and hosts an annual world-class championship. The area has seen the emergence of some of Canada's best bikers. It's not a big mountain in the alpine sense but since you'll be biking it you really don't need Banff, Everest or K2... If you only have a few days, I'd stick with this one.
If you have many days, the Charlevoix region not too far from Quebec city (in canadian distances anyway) probably has a lot of hidden gems. The area is very hilly (for Quebec) and the landscape is breathtaking.
Bromont (closer to Montreal) is also very popular for mtn biking and is also a draw for many types of cyclists (they have a speed cycling stadium and national training facilities). If you have a lot of time, Morin Heights, Val-David, St-Jean de Matha (Montagne Coupee) and Val-Morin are also often talked about but seem less crowded than the big tourist spots. But that's all getting farther away from Quebec city and closer to Montreal....
I've no idea what Ontario has to offer.

Dear All
Many thanks for all the replies! In the end I've decided to head for Hardwood Hills in ON for a few days as Mont Ste-Anne is shut till the end of May :-( and I'm there next week - typical. A real shame as it sounds spectacular - I'll have to come back when it's open!
Thanks again for all the advice - hopefully of use to others too when searching - and if anyone's in HH Thurs/Fri/Sat next week hopefully see you there!
Dear All
Many thanks for all the replies! In the end I've decided to head for Hardwood Hills in ON for a few days as Mont Ste-Anne is shut till the end of May :-( and I'm there next week - typical. A real shame as it sounds spectacular - I'll have to come back when it's open!
Thanks again for all the advice - hopefully of use to others too when searching - and if anyone's in HH Thurs/Fri/Sat next week hopefully see you there!
Dear All
Many thanks for all the replies! In the end I've decided to head for Hardwood Hills in ON for a few days as Mont Ste-Anne is shut till the end of May :-( and I'm there next week - typical. A real shame as it sounds spectacular - I'll have to come back when it's open!
Thanks again for all the advice - hopefully of use to others too when searching - and if anyone's in HH Thurs/Fri/Sat next week hopefully see you there!