You will want to stay downtown, on a subway line. Try to stay west of Yonge St. (east of Yonge downtown is kind of sketchy). But not too far west because that gets sketchy too. The Yonge St. corridor is where I would stay if I had to live downtown. Bloor St. west is also a good bet. Lots of shops and good restaurants around there. Union station, as mentioned by the previous poster is also convenient.
The tourist destinations you named is all over the city. The zoo is way out in the east. I don’t think you can get there by subway, and it’s a friggin long bus ride out to the zoo from downtown. Center Island is vey nice in the summer. I don’t know how it will be like in the winter (November) but there is a petting zoo there and Centreville with fun kiddie rides and a beach and bike rentals. I have no idea whether any of that will be open in November so you’ll have to check the website.
Science Center is also fun, but it’s in mid-town. I can’t remember whether they’ve opened a subway line there but in the past it was only accessible by bus
Fantasy Fair at Woodbine Centre is another fun indoor option, if it’s too cold to hang out outside. It’s far, and best reached with a car.
Also a trip up the CN tower might be fun if it’s a clear day.
If it’s snowing, then ice skating at Nathan Phillips Square might be fun.
A lot of the options you mentioned are quite pricey. I doubt your not-yet-two year old would remember any of it. When DD was under two, and we went home to Toronto in the summer, we just brought her to the nearest playground and let her toddle around picking up leaves and sticks. She definitely did not remember the zoo. I think we paid over $100 for admission tickets and she was awake for only the morning (around 3 hours) and then took a 2 hour nap, thereby pretty much wasting half the day. And she can’t remember any of it now.