Child-Friendly area to live in on Hong Kong Island

Hello

We will be moving to Hong Kong in summer and desperately need some advice:

LIVING/RENT:
- Which area is good to live in for a family with two small boys (aged 2 and 4) with possibilities to go outside – park or beach or cycling or anything nature
- Of course it would be nice to have a pool, a playground, a supermarket with western products and a gym in the building or close by.
- If possible not more than half an hour for my husband to work (Connaught Road / Central) by public transport
- Does anybody know a good estate agent for expats?
- How high should the budget for a 3 bedroom flat be? (the employer is paying)
- Other things to put on the priority list for searching a flat to rent?

Any other important info that we should think of while moving from Switzerland to Hong Kong?
Any input will be highly appreciated :-)