Welcome to SSH!
The yellow dots in the map are launch areas that you might want to get familiar with.
For fishing areas around CL you can try the following:
1. South side of Mud Lake
2. Near bridge of Nasa Rd 1.
3. Clear Lake/Kemah Channel
4. Kemah Flats - 29 32.510, -95 00.900
5. Seabrook Flats - 29 33.500, -95 00.970
6. Seabrook Tidal Tubes - 29 33.560, -95 01.160
For Mud Lake you can launch in the Clear Lake Park, but I prefer to launch in the public boat ramp in Nasa Rd. 1 and paddle to Mud Lake. Same thing for Nasa Rd. 1.
Clear Lake/Kemah Channel you can launch from the public boat ramp in Clear Lake Shores or under the 146 HWY bridge boat ramps. One thing to consider from Clear Lake Shores is your car needs to be out of the area by midnight if fishing the lights.
For Kemah and Seabrook Flats you can launch from Todville Rd and 10th St or from boat ramp under 146 and paddle your way out the channel.
For Seabrook Tidal Tubes you can park in the area next to Todville Rd. Due to rain and cars visiting you will find big deep holes that can make it difficult to park your car close to the water unless you have a 4x4. Last weekend I tried with my Pathfinder and I kept spinning my wheels, so I had to carry my yak.
I never tried Taylor Lake, but that is another option. Also, I saw a post from DelSol recently of fishing the Clear Creek area. I have done shore fishing from Bay Area Park with lowsy results and you should do catch n' release only there due to water pollution.viewtopic.php?f=8&t=185085
That is all I know about fishing the Clear Lake area.
For Galveston you might want to read more about:
1. The CauseWay
2. Offatts Bayou
3. Sportsman Rd
5. Pierce Marsh
6. Tiki Island
7. San Luis Pass
Other places that I have not explored is Texas City. There are a couple of places around there people fish often.
To get more details get your Hook n' Line maps for West and East Galveston Bay Kayak and Wade Fishing Guides. They are about $11 dollars each.