Nobody will ever agree, because it's all a matter of perpsective - whether you are looking in or looking out from a particular area.
For example - for me, from the San Jac river on I-10 heading north to 90 and east to Beaumont and then from 12 to the LA state line and everything south is SE Texas. Some will argue that the line extends up 146 to 105 then east. That's a definite gray area.
From Galveston bay to 59 going south to about Alice, then down to Falfurias then over to the south end of Land Cut is the Gulf Coast region. There are two sub-regions - the upper Gulf Coast from San Antonio Bay heading north and east, and the Coastal Bend region from San Antonio bay heading south.
East Texas is essentially 45 north from Houston to Dallas on the western side, I-20 on the northern side and 90 on the south side. Like the gulf coast, it has different sub-regions - the Pine Curtain, Redbone Country and just East Texas.
I-30 from DFW up through paris and Powderly is the western edge of Northeast Texas
I'd call North Texas as I-20 on the south, eastern edge is the border of Northeast Texas, and western border is Abiline to Childress.
Panhandle is essentially from Childress to Plainview to the border and everything north
West Texas/Llano is from Plainview to Ballinger to San Angelo to Del Rio on the east, all the way west to the Rio. Subregion of that is the Trans-Pecos region west of the Pecos river.
Central Texas is Del Rio to Abeline to DFW to about Seguin on the eastern side, following 181 south to 59 at Beeville, west to Cotulla (or maybe Pleasanton is a better border?) and then Eagle Pass Del Rio, north back to Del Rio. Sub-regions include the Hill Country (with an eastern border of I-35 and western to wherever), Blackland Prairie/regular Central Texas and whatever that region west and south of San Antonio might be called.
Valley South Texas is everything south of Eagle Pass (maybe Del Rio?) to 37 on the east, 77 south to around the Land Cut area. RGV is the handful of counties from Brownsville north to around Rio Grande City.
But that's from my perspective. Somebody posted above about Brady or whatever being 200 miles close to Louisiana than El Paso - but everything is 200 miles closer to something else than El Paso, because that place is hell and gone from anywhere. Hell, El Paso is closer to San Diego than it is Beaumont.