Between Austin (not on I-10) and NOLA, the interesting places would be San Antonio and Houston. I am a repeat visitor to both cities, there is always something going on, always something to do in each.
Between San Antonio and Houston, and Houston to New Orleans (usually I was going to Biloxi) I'm typically covering ground as quickly as possible. It seems like I-10 was routed across the Texas coastal plain to bypass anything of possible interest. What I find interesting in Texas is mostly west of I-35, or between US-190 and I-20 east of I-45.
Leaving Houston to the east, I'm usually trying to get past Baton Rouge before the afternoon rush hour. I suppose a stop at Lake Charles could change that timing, and if your goal is to get to New Orleans, rather than trying to get past it while the Interstate is not jammed with local traffic, it could be worthwhile to spend a whole day driving SR-14 and US-90 from Lake Charles to New Orleans, because many of the the pre-Interstate tourist attractions are still hanging on. Kind of like following Old Route 66, but through muggier country.
But from Austin to Houston, I would not drive I-10. I would follow US-290, explore it for what might be along the way.
Tom Test
Itasca Spirit 29B
