Let's see...Based on what I know from my civilian job with a local major cash services company, in this city there are:
17 x TD/Canada Trust ABMs;
23 x full-service RBC;
35 x RBC Cash-Counters;
12 x BofM ABMs;
11 x BNS;
14 x Credit Union (includes Saskatonn Credit Union and the others); and
about 30 x CIBC, which we don't service anymore.
Then, there are about 12 'private' machines, some of which we service, but none have more than 1,000 bills in them.

So, that makes about 144 machines in a city of 200,000. Canada has more ABMs per capita than any other country in the world.
Depending on how well the Bank manages their machines, most have about 2,500 bills go through them on a weekly basis.
(In my humble opinion, TDs are the worst managed, RBCs are the best.) In total, there would be about 360,000 bills weekly going through Saskatoon's ABMs.

The banks normally have a surprisingly small amount of cash on hand at any time. For security reasons, I can't really say how much. (but there is usually more in an ABM!)

I can't guess how much is in circulation elsewhere in the city, with businesses, stores (floats), bars, etc, plus whatever people carry or hoarde.