Areas in and around Toronto for family

Family of four looking to visit Canada for six months and maybe longer in the future. My wife and I are looking for city or area recommendations near and around Toronto. We want to be within 30 minutes of the city Center by car or public transit. I would love to live in the city but our rental budget is $1300 max for a 2 bedroom.
Would we need a vehicle if we lived in the city Center of Toronto?
We also don't mind areas near Montreal or Vancouver.
What areas should we look into?
We live in Southern California and love the vibe, beaches, and weather.
We want to be close to the city life but we understand our budget may not fit that lifestyle.
We also do not mind a 1 bedroom.
Any advice on moving to Canada, areas to look into, or just any insight you can help me out with making our decision it's is much appreciated.

HI,

already the rent in toronto is over CAD$2,200 for a 2 bedroom apt.
1 bedroom probably CAD$900 depend the area.
Montreal is cheaper,
Vancouver is expensive
there are more cities as mississauga close to toronto where you can find a little better price to rent.
in Toronto area is faster to move by public transportation.
$3.5 dollar / fare in cash, two hours free to transfer another route.
(monthly pass $148.5) PRESTO CARD