I'd say you can explore Stanley/Repulse Bay quite easily by hopping on a bus or taxi from Central. What the LM is great for is "relaxed" surroundings because it's a bit removed. There is a large bus terminal right beside the hotel so it's quite convenient but plan for a 15-20 (min) bus ride to Central or Causeway Bay if you're going that way. <10 min for a $10 USD ride by taxi.

No experience with SPG Gold, though.