that's an interesting question mate, Broome can have waves on a cyclone swell but technically isn't a surf destination. I reckon Barrow Island is the most north I've surfed but personally never planned a trip further than Exmouth for a wave.
There's a few spots on the islands around dampier, but most need a decent swell to work. The place has no crocs, but is full of tiger sharks and curious bronzies more than big enough to ruin your day.
Apparently Port Hedland is getting a wave pool. I'm guessing that would be kept fairly free of crocs.
Furthest North I have had waves is karratha but you will need a boat and some serious local knowledge if you go much past Canarvon....a lot of curious wildlife around as well