Normally Broken Cart is fine but who knows in these Covid times. Long Plain rd will close after the long weekend in June unless it gets too wet or there is an early dump of snow.
Check with Tumut Visitors centre on 0269 477 025.
You have to book camping spots in National Parks and Blue Waterholes is heavily booked. Check availability on line or phone 1300 072 757
Cooleman mountain camp is the closest (about a 10 minute drive to BWH) but can also be booked out on weekends.