I was in Broome for 4 days last July and unfortunately agree with you about the tackle store. I loved the place though and I can highly recommend the Boab boat hire up there. We hired the centre cab for a day, they picked us up from our unit, drove us to the beach where we launched, and then were there on the beach to pick us up at the end of the day. They even rang us the day before to see if we still wanted to go out the next day as there were forecast 12 - 15 knot winds in the morning and they were willing to give us another day with a better forecast. Being from Sydney the wind was not an issue and by lunch we were fishing in mirror like conditions anyway. Plenty of mackeral, queenies, and a few different tasty bottom fish such as mangrove jack, stripeys, trout etc.
It looks like you tried near the wharf. I would have loved to have had a session there as heard plenty of good stories, but the distance from where we were staying and my fishing "credit points" were getting low.
If anyone heading up that way and has the time I also recommend making the trip further north to Cape Leveque (from memory 3 hour trip by 4WD). Magic place with great fishing and I would love to tow a boat there in the future.