There are many great places to fish in and around Cockroach Bay. The islands south of the channel hold lots of fish. In and around Snake Key and Beacon Key during the spring is outstanding. Even the opening of the channel will hold fish coming out of Cockroach.
Little Cockroach Bay just north is also pretty good. Very shallow, but some of the islands have cuts, like Big Pass. Those cuts are productive, many times on the high-tide peaks, the turn-around of the outgoing tide can be off the charts for snook.
If there is lots of grass, or if I need to get under and in the Mangrove trees, I use a DOA Jerkbait, Texas-rigged in the Arkansas Glow (#406). That is Killer! I sometimes use a Mirrolure Mirrodine in the XL size in the color of #18 or #49. Just watch your tides so you give yourself enough water to get in and out. As far as live bait, Scaled Sardines work well. The photo is a DOA Jerkbait Arkansas Glow.
One of the best tools you will ever find for fishing, hunting, and general study of what's around you is Google Earth. This link was done in the application running in Chrome but it works fine in any browser (probably). It's a close-up of the Cockroach bay and surrounding spots. EG Simmons Park is here, and it's one of the most popular kayak anglers' launches.