Surferboy,
I agree with Jim, great idea & you will easily get well past Wollongong on day 1.
It would make the second day more leisurely.
Some thoughts.
Sydney locals will know the best route out of Villawood when it gets closer to Easter. The place can be frustrating for visitors depending on the time of day, the latest changes in toll ways & current detours around any major construction. It can seem to take forever sometimes but once you're out, you will enjoy the relaxing drive down the coast.
The South Coast is a very busy area around Easter. Many people (including half of Canberra) take the opportunity to get away for a few days before winter sets in.
Kiama has the famous blowhole they now say is the largest in the world, but it could be a good spot for a cuppa or lunch anyway if it's close to that time.
I have only ever stayed at a private address in Nowra but I'm sure there would be plenty of suitable accommodation. I have stayed at a caravan park at Sussex Inlet a couple of times. It's about 40 minutes further heading south & just off the main road. A smaller town than Nowra but has all you need in a quiet holiday spot.
Lake Conjola (between Nowra & Ulladulla) is very well set up with family tourists parks that are well regarded & very popular.
Mollymook & Ulladulla are typically pleasant tourist spots along the track. I've stayed in a caravan park in Ulladulla when there was nothing else available within miles (hadn't booked ahead) & it was great.
South Duras is another location set up like Lake Conjola with large parks to accommodate the family tourists. They are highly rated & offer beach frontages.
Batemans Bay is the gateway to the South Coast for Canberra. Many people own weekenders there because it's only a couple of hours away. You will see a lot of vehicles in the Bay with ACT registration over the Easter break. Accommodation would need to be booked well in advance. There is a zoo at Mogo (just outside the Bay). I haven't been for many years now but if you like zoos & have kids with you, then it's good to see.
The trip from the Bay to Canberra can be slow at peak times due to (mostly Canberra) traffic. It's also a very steep climb to begin with to get over the Clyde Mountain. There are a few places along the way for pulling over if your car overheats but finding water could be a problem. The Kings Hwy is well known locally for the number of casualties it has claimed. I think the road surface is mostly quite good but the last time I went to the coast I could not believe the risks taken by some drivers & at ridiculous speeds around blind corners. Be wary.
Further south past the Bay is more of the same - scenic & pleasant driving with places of interest. If you & the car somehow end up arriving in Sydney day or two earlier you could continue on south.
Narooma & Bermagui are fishing towns with day trips to Montague Island (details on Trip Adviser). I did a fishing day trip to the island 45 years ago & it's still popular.
Merimbula & Pambula are almost adjoining holiday towns famous for their beautiful beaches.
The trip from Merimbula to Canberra is via Brown Mtn. It's a magnificently scenic (very hilly) road with through Candelo to Bemboka, then it's a steady climb up the Snowy Mtn Hwy towards Cooma, then another good hour to Canberra with everything in your favour.