GTA consists of multiple municipalities, I can only speak from my personal experience about Toronto and the following should be considered subjective based on my opinions:
- I feel that the work from home situation which many people are betting their life decisions on is going to slowly phase away atleast for most major professions like banking professionals.
- A downtown condo right now if you are planning to live in a condo/apartment for a few years is going to get you in at a very low rent controlled price that would be really good.
-A lot of downtown toronto has issues with homelessness, drug abuse, and 'non-friendly' elements on the streets here and there, there's also some neighbourhoods in downtown that I'd like you to specifically avoid - Moss park, West end, most places on and around Dundas street between river street to the east and Spadina street to the west
-The area that I feel might be best for you would be roughly in an imaginary rectangle between Yonge St, Spadina St, King West, Queens Quay W
I agree with someone that you should atleast get a 1 bedroom + den or even a 2 bedroom, you would definitely get a 1 bedroom + den in your budget and may also get a 2 in your budget if you're lucky in the area. Your budget allows you to live right across from the waters and believe me from experience it's a blessing to take your children out for a stroll on the water front.
-There are public tennis courts scattered across downtown, you just need to know where they are and depending on the time of the day there's usually splace to play, there is a couple in Moss park which will be roughly 15-20 minutes walk from the area I'm suggesting. There are quite a few near Rosedale metro station which is 15 minutes away from union station(union station being inside the rectangle I mentioned)
-If you don't want to stay in the city, (believe me, cities are a lot dirtier than the suburbs) there's a lot of options there too in your budget, but then again there are so many places that will be in your budget in the suburbs that you'd need to think of more requirements maybe.