The Espresso Room (New Row)
This shop used to be called New Row Coffee, but it seems to have been bought by an independent chain. I was a bit apprehensive initially as New Row had already been bought and things had changed for the worse, but my last visit after the second change of ownership and new rebranding produced very satisfactory flat whites and some delicious cakes that we enjoyed greatly.
The space is very tiny, so you should probably expect sharing a table with someone else unless you're on off-peak times. I used to come here with my laptop early in the morning to think about things while having a flat white before going to the office, which was fine because there was plenty of space at that time, but come any time past 12h and it's impossible.
I believe there's still no wi-fi, and cell reception is spotty.