CMGogo:
I take it from the above that you want to go the private route whether or not your company's insurance covers maternity costs - it is nothing to do with whether it is a preexisting pregnancy or not
(unlike coverage for illnesses). Usually, they don't unless you are on a expatriate package with the largest multinationals. Since it is the birth of your first child, I take it you won't mind spending an extra dollar or two on going private.
Beware though that private hospitals are very overbooked as a large number of wealthy mainlanders like to give birth to their children in HK (for the residency). The best private hospitals are the HK Sanatorium and Hospital (in Happy Valley), the Baptist U (in Kowloon Tong), and a popular one with expats is the Matilda Hospital (on the Peak). You can google all of them.
Your wife will probably need to set up an appointment with a good obstetrician. Different obstetrician are "attached" to different private hospitals, so you need to see whether you will be choosing the hospital first or the doctor first. Make sure you make a provisional booking with the hospital based on your wife's delivery date - of course you can't be very sure if she is not having a caesarian section, but the doctor could give a good guess and book a bloc of dates accordingly. I mean it - book, even months in advance, or you run the risk of not having a room at all, or if lucky, just being in a general ward at best.
From what you said, I think you are better off living on HK island - IFC is in Central. If you are gonna have a kid, I wouldn't live in Causeway Bay. Depends on how long you will be here for - will you still be here once your kid reaches walking/running age (age 1.5 and above)?
If so, Mid-Levels is out (although some people would think differently). Go to:
1) Happy Valley - right where the HK Sanatorium & Hospital is, prices are right, there is more of a community "feel" there.
2) Jardines Lookout - for toddlers, the best estate would be Cavendish Heights, go to "Centaline Hong Kong" (large estate agent)'s website to see if there is anything that small and within your budget.
3) Somewhere on Kennedy Road - Still Mid levels but not the side of Mid Levels most people think of, but on the other side of Garden Road. Quieter, more space.