Hi Mark,
+1 for the Walls of Jerusalem. A very special place, plenty of options for walking from a base camp (which would be 6 km in at Wild Dog Creek, or a bit more at Dixons Kingdom). If you have a hire car, it needs to be one you're allowed to take on dirt roads (not all companies have those).
Pine Valley could also be a great choice, but it will cost a lot more, if you get the boat up Lake St Clair to Narcissus. $50 per person each way, and they can be very unreliable in non-peak season. They can just cancel boats at the last minute if they have less than 6 people, unless you're happy to pay $300 each way. They also have to cancel the boat if the weather is not good enough. On the other hand, if you get the boat in, and plan to walk out, you'll know where you stand. You can camp at Echo Point on the way out.
You might still have snow at Pine Valley, more likely up higher on mountains you can see from the helipad. How is your navigating? The Labyrinth isn't a place to be when the mist comes in if you're not excellent at it. I'd strongly recommend a GPS, as it's tricky to find the way down if the track has enough snow on it. Someone disappeared there a few years ago in a snow storm, and was never found.
I'd choose the Acropolis from Pine Valley instead, if visibility was going to be dodgy. You can go up the track as far as you want if there's snow, without going all the way to the top. You may have wonderful views from the plateau part way up.
Lees Paddocks is another favourite place for beginners. You need to get permission from the owners, which is easy as long as they don't have a family do on at the same time. It's 7 kms easy walking in, with a hut for shelter if you need it. You could well have snow on the mountains that tower over the paddocks, and on Pelion East, which is (sometimes!) visible up the valley. You can explore waterfalls in the area, go upstream to check out Waddleys Hut, and/or go up the 'Venetian Blind' track, to Lake Ayr +/- Pelion hut. The road in is still 2wd, but getting pretty rough.
Or, you could do the 12 kms up the Arm River track to Pelion hut. You could then do day walks up Oakleigh (fantastic!) or maybe to Pelion Gap or partway up Pelion East if he's up to it. Stunning if there's still snow about. You could start your son dreaming of doing the Overland Track one day, and meet some people who were doing it.
And absolutely have a plan D, on the east coast, in case of poor conditions. Another choice would be Freycinet. E.g. 2 nights the other end of Wineglass Bay, with a day walk up Mt Graham in between.