I had this problem.

I wanted to go to a maternity hospital which is about 25 minutes away. There is a general hospital with a maternity ward about 10 minutes from me which I've only had bad experiences with (sent my DD away with a broken foot saying it was 'normal', ended up on crutches for a month after the GP sent us to another hosp.. Sending DS away with a broken knee cap, I knew it wasn't right and took him to another hospital, he was in a brace for 6 weeks, sending my cousins DD away when she was having heart palpitations THREE times, knowing there is a family history of SVT..she went to the RCH and spent a week in there and has had 3 heart surgeries! You can see why I wouldn't birth there!)

Maternity hospital wouldn't take me because I wasn't in their zone.
I even went there with a letter from the GP as I had a threatened miscarriage and they wanted me to see their early pregnancy clinic, but still would not admit me there for general care and birth.

I ended up in a private hospital just so I wouldn't have to go my zoned hospital!

Having said that though, I have heard heaps of people say they got to choose their hospital regardless of zone.. so it couldn't hurt to try!