We have stayed at the Big 4 in Dubbo.  They have drive through sites.  Depends on how long you intend to stay I guess.  The Big 4 is reasonably close to the Zoo.

Also have stayed in a cabin at the Top Tourist many years ago but it is closer to town and right on the river where people like to congregate (if you get my meaning).

That's all I can help you with as I haven't stayed at any of the others.

We would recommend Peak Hill Caravan Park even though it is 70km down the Hwy. Certainly meets your stated requirements then some. Dubbo, been there done that and never again.

We always stay there when heading up the Newel and stock up at the local butcher and the home made cakes/biscuits at the craft shop at the southern end of town. The hand made while you wait Spring rolls in the café near the butcher are great, as are the Chinese meals in the RSL club just a few hundred metres from the park.

We just love the smaller country towns.

BTW Leighton and Pauline bring around scones with jam and cream about 4:00pm each day so have the kettle boiled for that arvo cuppa.

I wonder if Caravan parks could put  their rates up out  the front, on a board or something...It would be very handy then one could decide weather or not  to go in.....Lets be fair Dinkum some are very ordinary...The experience I had at Bribie Island was terrible at $30.00 per night......I ended up leaving and going to the Council and parked out front....Free! The site was  so small..I need a drive through

We have an NRMA Caravan park guide which lists caravan parks around Australia, with their prices (usually a bit out of date!) also rates them with stars. While the ptices arent always accurate, it gives us an idea of which park in town is more expensive than others, and what facilities they have.
Not all caravan parks participate mind you. Its a handy.reference, updated every year or so.