Hoping to find out which aster this is that comes back each year under an oak tree. The petals are a subtle lavender color.

Are the leaves rough to the touch, or smooth and almost waxy?

If the leaves are rough, it looks like Late Purple Aster (Symphyotrichum patens):

Late Purple Aster (Symphyotrichum patens)

http://www.missouriplants.com/...

If they are smooth, it's not S. patens, but could be Smooth Blue Aster (Symphyotrichum laeve) perhaps:

Smooth Blue Aster (Symphyotrichum laeve)

http://www.missouribotanicalga...

Both species usually have darker blue violet (ish) flowers, but it's not unusual to see individual plants with much lighter flowers, all the way to pure white. Both also typically occur in open woodland-type habitat, and sometimes in prairies.

Are the flowers fragrant? If so, it could be Aromatic Aster: http://www.wildflower.org/plan...

There are a few listed in the database: http://garden.org/plants/searc...

Or perhaps this Texas native?: https://npsot.org/TrinityForks...

The leaves are rough to the touch. They look much like the ones in photo for Late Purple Aster (Symphyotrichum patens)

and they are shown as native to Texas here: http://plants.usda.gov/core/pr...

And I noticed that it does have the woody-ish stems that grow from the rhizome. This picture is from last year.

Aha, It does look like Late Purple Aster (Symphyotrichum patens)

Thank you Kent and Lin!

Yay! I'm closing this one as solved!