I live in Huntsville and have a bunch of pine trees in the backyard that; cast a lot of shade, likely make the soil acidic. The grass planted was St. Augustine sod but I want to change that if possible because the large trees and lack of sun are not helping the gas to grow.

What's my best option for seed to spread?

St Augustine

St Augustine is the only actual grass that tolerates Texas temps and humidity and the acidity of the needles and such.

Cut down some trees to let in light or put down mulch/gravel if you don't want bare dirt.

You've got a mature forest environment that isn't going to grow grass.

That's what I was afraid of....

Next question, when's the best time to plant/sod the area?

I have same and went natural with ferns and shade plants. Mowing grass is over rated.

Could you expand on this a little please? I'm no dummy but I don't have a really green thumb

I'm up at Lake Livingston and under a high canopy of pines with high to medium shade. I initially had some sun and put in sun loving plants like crepe myrtles and fruit trees and grass but as the pine canopy grew and expanded they started failing and I had to adapt to more shade loving plants. I minimalized the grasses (and the mowing) and promoted the pine needle base forest filled with native ferns, iron plants, and ivies and brought in color with red buds, dogwoods, azaleas, spireas, etc. I love my pines much more than I loved mowing my grass and now I have more time enjoying it all rather than maintaining it.

Azaleas love acidic soil, if you get the Encore variety you'll get multiple bloom cycles per year.