Haven't lived in Ontario but saskie has and will hopefully chime in on this. My guess would be the northern portion away from most of the urbanization. Check out some of the guide hunting in Ont. and see where they are taking their clients. It may give you some clues.
Chester is bang on wrt getting away from the populated areas; especially with adult moose (calf moose tags are generally available over the counter). Ontario has good moose numbers but with such a high human population getting a tag is tough. Basically if you can drive there in a day from Toronto/Ottawa you'll be a long time waiting for a tag
It really depends on what you're after: E Ontario/Ottawa Valley (Ottawa/Peterborough/Pembroke) has fantastic white tail, goose and turkey hunting but moose is tough - both in numbers and access to tags is right up there with winning the lottery unless your in a group draw (and even then its still a long shot); bear is present in huntable numbers but its won't be making the short list of bear hot spots anytime soon.
Northern Ontario (ie: North Bay/Sudbury/Thunder Bay) has great moose and bear...but getting drawn for moose is still a pretty long shot
Southern Ontario (GTA/Windsor/London/Waterloo etc)...forget it. Decent deer and turkey but access is next to impossible.
My reccomendation would be NW Ontario - Dryden/Kenora...good white tail (I would say slightly fewer numbers than the Ottawa Valley but they're the same big-bodied, thick racked western strain that we have in N Sask); great bear hunting, good moose hunting and infinitely better chance of getting drawn for a tag.
I would have to second saskies sugestion of north western Ont, anywere above Thunder bay eisier to draw moose tags and in some WMU you can draw extra WT tags as well.
I live in central Ont and it is hard to draw a tag for moose. if you want extra tags for WT I would say more to the farming areas around London in South western Ont. There you can get up to 6 deer tags.
The record books, that are put out by Boone & Crocket and Pope & Young and where I live is Henry Kelsey they are a great way to research a state or a province for big game. This does take some time but the knowledge it gives you, can be very valuable. Not all hunters have their trophies recorded, as where I live after the Hanson Buck became the new world record typical Whitetail, we saw a flood of hunters and now that has happened, some hunters are shying away from the record books but...