I used to do a lot of business with Bruce at USA Racing Engines near Hobby Airport. But it's been years.
I've never had any work done there, but friends have had work done at Houston Engine and Balancing in Pasadena.
The above shops do mostly race engine work, not sure that's what you need. In the same category are Faerman and Nickens.
I had some basic machine work for a stock performance rebuild done at B&G Machine in Alvin. I had that done when I worked in Alvin, that's been a long time too.