A good 5-7 blocks would be a safe bet. If the wind is coming out of the north, a mile might not be far enough, but the wind general comes out of the south to southeast.
I lived in Nottingham Country about 4 blocks south in the old section with the alleys, never noticed the noise and we were out at the pool all the time.
If you wanted to be sure, try to stay south of Kingsland Blvd. Let me know if I can assist you as I know many of those older Katy neighborhoods (lower taxes there as you well know!).
Bernstein Realty, Inc.