Places generally along the South Freeway (I-45), and south of the Ship Channel, including Clear Lake, Deer Park, Freindswood, the Hobby Area, League City, Pasadena, Santa Fe, South Houston, and Texas City.
Wow, I'm glad to see so many other people googled to find out what was making strange nocturnal chirping sounds. I listened to audio of all the critters suggested over the past 15 years since the original post, and I finally found the source of the sound I hear each night here in Austin. And the winner is.....RIO GRANDE CHIRPING FROG!! It makes me happy knowing there are tiny frogs outside my bedroom window.
Lots more great information about the Dawson Lunnon Cemetery here: https://houstonhistorymagazine.org/2015/03/dawson-lunnon-cemetery/
It's in pretty good shape as of 2020. A beautiful little forested nook to visit in the middle of a bustling city.