The Peak - once you step away from the touristy Peak Tower and Peak Plaza buildings - is one of the most underrated hidden gems of Hong Kong. Very quiet, nice paved and shaded roads (with very few or no cars) to walk around; and the view towards the south side of HK Island is totally different from your view from the Ritz Carlton.
And the Peak Tram is quite interesting and an unique funicular, with its greatly slope. I have rode a lot of funiculars in the world, and still haven't rode something similar. Definitely worth riding, even if you're surrounded by tourists from China.