3 weeks in Canada/US during August

I’m going on exchange to a town near Toronto this fall. Before it i was planning to travel around in Canada/US, I have 3 weeks to a month of free time.

I’m only 20 so I can drink in Canada but not in the US during my trip, Which is a bit of a bummer.

I’ve been thinking of going:

Chicago -> Toronto – > Ottawa -> Montreal -> Quebec city

To then go back to Toronto and start my studies. Later during breaks or after the exchange i could discover US east coast as then I’m 21.

Is this a good idea or am i missing out on something ? Should i explore British Columbia or some other part as well?