Hmm that's a big ask... You won't really get any holiday parks within that distance - if there are any, the tend to be residential, not for holidaymakers. 30 mins public transport would mean North Sydney through to Chatswood, Bondi and nearby beaches, as far out as Strathfield or possibly even Parramatta and maybe as far south as Hurstville.

But public transport isn't fun - if you're coming to see the city, I would recommend staying in the city. Even getting around the city centre is quite exhausting.