Where is the closest public cricket pitch to Bardon?

One (Rainworth) option is:

Norman Buchan Park (Griffiths Park, Norm Buchan Park) 53 Rainworth Road Barbecue (wood), basketball/netball facility (hoop, basketball keyway court), cricket facility, picnic area (Baroona Road), playground (Baroona Road, Rainworth Road), toilet (Baroona Road), water (bubbler/tap)

See: https://www.brisbane.qld.gov.au/facilities-recreation/parks-venues/parks/parks-suburb/bardon-parks

There's a cricket pitch in Jubilee Park in Bardon. However, I'm not sure what you mean by public. There is a cricket club based in the park who seem to maintain the pitch and play there on alternate weekends.
Bowman park has a cricket pitch and nets available for public use.