As mentioned previously the Grays Point and Yowie bay boat ramps are the pick.
Yowie bay is probably the best, but no fish cleaning or wash down facilities.
Grays Point is a little further to get too, but has wash down facilities, but no fish cleaning table.
There also is Cronulla, but only for small boats, pick the tides and limited parking.
Both Yowie bay and Grays Point have pontoons. Grays point also has a beach that you can pull your boat up on.
As for times and with all boat ramps, you either need to go at night, get there early or I often go around 11:00am - 12:00 noon and jag a spot, when all the fisher people start heading back.
Port Hacking is one of the best waterways around for boating leisure. But, I have found, is a little hard work with fishing.
Happy boating.