If the backyard faces north that means it is shaded by the house for much of the day. That’s good if you don’t like high temps. Not so good if you like to garden or have a pool that will be shaded.
The garage facing south… no opinion on that.
For me, what would be more important is the direction of the roof line. Having a south facing roof line (eaves run east/west) means you could upgrade to solar in the future. Solar panels work best if on a southern exposure. Unfortunately, our roof line runs North/south – so we’d have to settle for west facing panels.
Every home owner is different. Every home owner has differing priorities. I like to garden and would like to install solar someday. A north facing backyard means the panels would be in the front – so more visible from the street.