M.P.
I went to the Plano YMCA and my kids loved it. There is, however, the Allen Natatorium (http://www.cityofallen.org/parks/natatorium.htm)that offers swimming lessons and I hear they are great. The website for swiming is http://www.cityofallen.org/parks/aquatics.htm. The best part of that is the evaluation. They will let you know where your child should start, etc. I have several friends who are members of the Natatorium because it was across the office from where I worked and they love it - inexpensive and nice with tons of stuff to do.
Some of our really good friends' mom teaches swimming lessons at her house - or she used to. She lives in Whitesboro though so that may be too far for you to drive.
Good luck.