Henry Saw located at the Grand Lane, in the same building with the Museum of Perth and in the same complex as Toastface Grillah. 

I went there for a cup of flat white one rainy afternoon and purchased the last of what the staff called 'the best almond croissant in town'. Whether she is right or wrong, it was a pretty good croissant. The coffee (Ethiopia bean from Blacklist Coffee Roasters) was pretty solid, it was quite strong but not too bitter. I would love to go back and try their cold drip next time. 

PS: Henry Saw was the first known person to roast coffee in Perth. Thus the name of the cafe ;-)

Henry Saw also sells some vegan friendly wrap and three different types of kombucha. They built their own custom cold drip for coffee.