I hate to break it to you, but as someone who spent most of their life in the GTA (Toronto, Scar., and Durham Region) it's clear firearm owners/hobbyist are not welcomed in the city. You can try Gagnon Sports in Oshawa (I was a member there for about a year and a half) but they also require sponsors (you will be hard-pressed finding any range that does not require a sponsor). I got into Uxbridge Clays without a sponsor but your first year will cost you a grand and they thoroughly vet each new member application, but they have some of the best fields I've seen.
I had to make a decision, if I wanted to continue pursuing shooting (especially at a competitive level) I had to move from the GTA, and so I did (there were a few other reasons as well, but that was a major one). If you ever want to shoot anything beyond 250yards your only option is to join a league/class that uses the Borden Military Base, or crown land hours north, but I would not be out there by myself.
I am currently a member of Orillia Gun Club which is fantastic but comes with some limitations and it is hard to get in, and will also cost you 3/4 of a grand in your first year (most clubs I have dealt with have a one-time $400-500 initiation fee).
GL