There aren't really any zoos around Newcastle, except Kirkley Hall Zoo, Tynemouth Blue Reef Aquarium and Washington Wetland Centre; all are pretty small places. Kirkley Hall has the most diverse collection of the three (
see here), but very limited opening hours/ days; Tynemouth Blue Reef has Seals, Otters, Fish, Tamarins and a few other species, but nothing really special; and then Washington has a long(ish) list of waterfowl, Otters, Flamingos and Cranes (
see here) and lots of wildlife watching opportunities (and you'll get male ducks in their winter plumage).
I would give Yorkshire Wildlife Park about three hours to look around, but could be done on less, so you could visit another local collection at the same time, the ones you could feasibly do are;
-Tropical Butterfly House, Wildlife and Falconry Centre (Sheffield); has a diverse collection, and some quite rare species (in captivity); it has easy access to the motorway.
-Wetlands Animal Park (Redford); has a small collection mainly domestics, the only species which particularly stands out (well to someone from the UK) is White-fronted Capuchin (
Cebus albifrons; incorrectly listed on zootierliste as
Cebus capucinus), but this is quite rural and difficult to find from the motorway.
-Lotherton Hall Bird Garden (near Leeds); a small but diverse bird collection with a lovely café and some rarities; very close to the A1, M1 and M62 (if you were to go to Manchester from Leeds you would probably go down the M62).
-Tropical World (Leeds); a diverse(ish) collection, small aquarium, nocturnal house and reptile house, as well three indoor bird areas and a Butterfly House, good if there is terrible weather; it has good road links to Manchester.
-Harewood House Bird Garden (near Leeds); a small bird garden with a decent collection although much reduced in recent years, I would personally recommend Lotherton over Harewood due to a larger and better (well in my eyes) collection; got decent links to the motorway, but it us really on the wrong side of Leeds for the motorways.
-The Deep (Hull); at a push you may be able to do this one; a large collection of fish, some of them quite rare in captivity, and a few herps, invertebrates and some Penguins.
-Ponderosa Rural Therapeutic Centre (near Leeds); home to a few mammals, birds, herps, fish and inverts, it has a couple of unusual species, I've irrationally never visited; near(ish) the motorway.
-Chestnut Centre (Chapel-en-le-Frith (Derbyshire)); a small collection including some unusual mammals and owls, I've personally never visited; not to far from the motorway.
These are all I could think of that you could feasibly do. I don't really know what species are around in Australia, so can't help you in that sense, if you want anymore information feel free to ask

.
(And if you haven't booked accommodation in Manchester yet, I had a comfortable and affordable night in one of the Travelodges, although they definitely are budget accommodation).
Although I would recommend a visit to HWP any day, I don't think it would be very easy to reach from Manchester, as you're looking at about 6 hours of driving to reach it...
EDIT: I've had a bit of a think and if it is Gorillas you're after you could probably be able to get to Twycross Zoo one day (and you could if you wanted visit Tropical Birdland on the same day, as they're close to each other). You could also get to the Welsh Mountain Zoo I imagine.
P.S. And I hope you use this well, as it took me a while to write
.