I have a static on a quiet site near Dolguellau, and we spend most of the summer there.
You have Coed-y-Brenin, Mawddach trail, plus a huge/near infinite amount of footpaths and bridleways, including Cader Idris. There is plenty of walks an 8 year old can easily do. The precipice walks (old and new) are both good.
Beaches, I prefer Fairbourne opposite Barmouth. The village is not great, but if you head more towards the river you’ll have plenty of beach and a lot quieter. As someone has mention Barmouth gets rammed on a sunny weekend, with the roads full, plus it has suffered from lack of investment away from the harbour. The beach between Aberdyfi and Tywyn is also great, and when you get away from the two towns, is pretty remote. Shell Island you have to pay for access, and frankly there are just as good free beaches around.
There are also lots of little railways a short distance away. Also Bala lake/Llyn Tegid is not far
My kids are 4 and 6, and there is lots of outside things to do with them. When it starts raining, then it becomes a little difficult! Just pack waterproofs!