C.B.
Lake Tawkawani- it's not really in Forth Worth- actually about 1 1/2 hrs east of Midlothian but it has the best lake for swimming(in my opinion) that we have been to so far. It has a nice, natural sandy bottom that is about 2 ft deep for quite a while and gradually gets deeper. There are tons of trees around and the drive there is really pretty. It's a state park so you can look it up to get directions. Some others closer: Lake Mineral Wells- that one was fun, but it is really small and the water isn't quite as clean(mainly from a marshy bottom) but it is a no wake lake because it's so small.
There is also a nice spot to swim at the Cedar Hills park lake(joe pool lake) I have only been to the part inside the state park, but it is nice. You will have to wear water shoes though. They have brought in gravel for the shore and it hurts your feet after awhile.
Have fun!
~C.