@ Phil -- If you're coming from London, HK's commutes will be way faster, cheaper and easier than what you're probably used to. We've very spoiled here.
People who live in Central / Midlevels talk about Quarry Bay or Kowloon as if they are on the other sides of the earth, but they're usually no more than 15-20 min by taxi, and 30 min by MTR. I work near QB and live in Kowloon -- on the OTHER side of town -- and I can cab it home in 20-25 minutes barring horrific traffic.
Much of HK is within a half-hour of QB -- just about all of the downtown areas of HK Island, as well as much of the South Side.
Your budget will go a long way in Quarry Bay / North Point -- you can probably get a 1,500-sq-ft flat in one of the nicer towers, like Grand Promenade, which has a seaview and clubhouse. (Not sure about pool, but you can ask).
Quarry Bay is not quite downtown, but there are certainly enough restaurants / shops in the Tai Koo complex. (Plus, as I said, it's not like Central is very far by London standards.) North Point is a bit more local, with fewer Westernized shops / restaurants.
The South Side is on the beach and more suburban / residential -- more expat-y, more green space, etc. Though you'll probably get a little less space for the same price.
Have you considered moving into a serviced apartment for the 1st month to take a look around? Some of my colleagues have stayed at the Harbour Grand complex, which is fully furnished. You can then do a better flat search from there.