Hate to say it but there aren't any public areas as such set aside. The Mudgee Visitors Centre will direct you out to Windeyer, Hargraves, Hill End etc.
There are a number of bridges, crossings etc. that the river can be accessed from but most of the better areas are via private property. There are some managed lands (TSR's) but they now frown upon any fossicking activities unfortunately. As one of Australia's most historic & reasonably important mineral wealth areas, we've lost the plot here as far as attracting tourists (geo-tourism).
They do allow fossicking out here:
https://reflectionsholidayparks.com.au/parks/cudgegong-river/
All I've found out there with the kids are some quartz crystals but it's good fun. However, the water is most likely to be too high at the moment after a few recent flood events. There's some gold around that area out there too but again private property access would be best.
