Got to stay in Kowloon. It IS Hong Kong. HKI feels like a relatively soulless business district like Canary Wharf or something to me. Just wander around the markets at night in Tsimmy and enjoy the feeling of being lost in the chaos.
Ten days might be pushing it a bit really
imo. Some nice beaches if that is your thing and you could do a trip to the mainland and to Macau. But after the peak tram and the big buddha there's not really that much to see. Go to Happy Valley races, that's pretty awesome.
Explore stopovers. You could do something like Dubai, Singapore or Beijing as well as HK. I've been twice, once for 5 days and once for 3 days. I think you'd get more out of the trip if you mixed it up a bit.
You can get taxis everywhere, they're dirt cheap.