Firstly, KT is quite accessible. It takes anywhere from 10-30mins on the bus to central depending on traffic. If you're feeling adventurous, you can take the tram which actually feels a lots slower but takes about 25mins also. Taxi's would take 5-10mins (for central, Soho, LKF) and would cost about £3.00. For Wan Chai, you would stay on the bus an extra 5 mins. KT is closer to Central than Pokfulam, which is another popular area and kind of the next estate over but less accessible as far as I can tell. Causeway bay is about the same distance from Central on the east of the Island but is much livelier in terms of bars/restaurants and ++shops. The nearest MTR is in Sheng Wan and is a bus/tram ride away which is a bit of a pain. There are plans to extend it to KT but that's going to take a few years.
KT has a public swimming pool but it's outside so it closes over the 'colder' months. The public gym is being refurbished at the moment so I haven't seen it. There is a small park that has a jogging track and a playpark and Tai Chi in the mornings. It has several supermarkets and a wet market (if you have the stomach!). 2-3 bars, lots of local restaurants, McD's, post office and library. Not much in the way of shopping.
There are a number of new buildings: Merton, Manhattan Heights, Smithfield Terrace, University Heights, The Belchers. There are also tons of older buildings. I live in a refurbished appartment in one of the older buildings, so it's much cheaper than the others. The new buildings I mention most likely have their own gyms and activities rooms?
Hope that helps. KT is not for everyone so I hope that helps narrow down your choices. Good luck!