Upvote:4
My experience, first and second hand, is that it depends. Some places in the US, especially those used to dealing with foreigners, will accept a foreign (especially Canadian) drivers license as ID. However there are likely to be quite a few that won't. I've even been in restaurants where the only allowed foreign document to prove age for alcohol purchase was a passport. (We weren't in there long.)
Assuming you are enrolled in an official course of study, this shouldn't be a problem however. Almost all education establishments issue student ID cards, which should suffice as photo ID. If that's not the case, you might consider looking into some other form of government ID. Some states issue cards purely for the purpose of identification.
If you are staying in the US for two years, you might want to consider getting a drivers license for the state you are going to be studying in.