You can launch from San Luis Pass County Park for free or down the road at the free launch at the end of Amigo Ln. Take a look at Google Earth. Not Google maps but GE. Download and install. Look at the history images from the past and see the bottom contours to fish.
The current (tide) and wind will be a deciding factor on where you go from launch. Left you can hit the north shoreline of the island where the wind is blowing the bait. You will need current to move the bait loose from the shore though as the wind pushes them into it and the fish will not commit to find them if the current is not there.
If you go right you can fish the marsh near Churchill Bayou. The current can get hairy with the pass close by so check the tides and times and be in the right area when it changes or you will have a hard paddle back or out. The wind can double the harsh effects of the current so check that too.
The closer you are to the pass the more water is moving and can get you in trouble if you are not familiar with the area. Try to bring a buddy. If not make sure you have a radio or phone in case you run into problems. Usually just anchoring out and waiting for tide or wind to change is best if you get in a bind. A TM helps too.
Haven't been down to Drum Bay yet but it should be the same as SLP being so close.
