Where can I take my 16ft. jon boat in galveston/freeport area for redfish,trout,flounder,blackdrum, and tarpon if possible

Tarpon??
Those would be at the end of the jetties, not a friendly spot for a johnboat at all.

Get a hooksetter map, and look for boat ramps in areas that look promising, running around the middle of that bay is not what I'd call a fun idea. Nobody is going to mark an X and say fish here over the internet. Enough potlickers already.

Texas City dike area and along the Bolivar peninsula (east bay) has good access to good fishing from smaller boats, just be careful and use good judgement. I grew up fishing Trinity bay out of a 14 foot flat bottom with a 10 hp Johnson. Been all over the Galveston bay complex in it, don't care to do it now, but many still do. A good map, as stated will help.

Alright thanks when I said tarpon I have heard of people catching in trinity bay.

Moses Lake off the Texas City Dike , I think Eagle Point Marina is just a Stones throw from it's gate and it's fairly Protected from the wind There's a Good Gut Southward to the Right of the Entrance of the Lake and The Texas City Dike gives a little Protection as well. Watch the wind and stay close to the Shoreline and you can have a Blast.

I have heard of that place befor but was not sure of it. Is it wadeable?

I personally Dont WadeFish but I'm sure that theres a shallow Bankline that is Wadeable Most all that Shoreline in that area has waders on it