"Can anyone weigh in via personal experience: how much Chinese would I need to learn to avoid getting pigeonholed to tourist areas in these cities? Is Mandarin spoken pretty uniformly?"

I think this depends more on the traveler than on the city/nation. I don't think there is anywhere that language necessarily pigeonholes you to tourist areas - it's simply how comfortable or uncomfortable it makes you.

That being said, I think you would have very good luck in Hong Kong, for obvious reasons. Beyond english accessibility, I find Hong Kong to be the most fascinating and interesting city in the world. I love to be there and miss it when I am not.

If you can find some kind of personal connection there - a meetup or hackerspace or ... anything ... it is definitely helpful and will get you off the beaten path much more quickly.