Here is a link to a Shannon Park Street View image -
Google Street View. I think that the church in the image is one that DND has put tenders out to demolish. Does anyone know the situation for the adjacent school (is closing it being considered?). It appears to me that a sheltered location could be found in this area (or artificially make it sheltered with dirt berms and trees).
Since I have recently been to the Toronto Rogers Centre and Toronto BMO Field, I can make the following observations:
1) The Rogers Centre has all public transit options and is probably the best location from the public transit perspective, but it is not a pleasant place to drive a car to (being in downtown Toronto, driving is nerve-wrecking).
2) BMO Field has lots of adjacent parking spaces and is much easier to drive to (it is directly adjacent to the Lakeshore Blvd which is easily accessed from The Gardiner Expressway). It also has very good public transit options, although not as good as the Rogers Centre).
From a vehicular transit perspective, the BMO Field location is much better. It is also in a central location and has good public transit. It is somewhat analogous to Shannon Park, in my opinion (the possibility of plentiful parking spaces, a fairly easy drive, good public transit, and relatively close to the central core).
Also since Shannon Park is currently quite desolate and run down, a very economical stadium could be put there without being overly concerned with the stadium appearance. It could be built quickly and cheaply.