The Geographic Center of Texas is located on someone's private property, somewhere in, well, the middle of Texas. Given that Texas is a fairly nonstandard shape, how the center was determined was left to the surveyors, but they calculated where it is. However, since it's private land, you can't get there from here. That did not stop the Texas Government from placing a historical marker at the center - the marker just mentions that the center is actually five miles away. What's five miles in Texas, anway?
As with any critical piece of historical significance, there was a scuffle between two towns over which one was "The Heart of Texas." Brady won over Brownwood. So, if you're traveling on US-377 between Brownwood and Brady, look for the marker. It's the one with nobody stopped by it (which is sad.)
Also, visit the Heart of Texas Park, which is just down the road and climb the observation tower. It gives a great view to the east and south, which is unfortunate, since the actual center is northwest.