What on earth are you going to do with “2-3 nights in each of the big cities in Texas”???
Don’t waste your time!
If you fly to Miami, DRIVE the Gulf Coast, to get a “flavor of the South!” You can pick your stops, based on what you want to see and do. Then, when you get to NOLA, grab a flight anywhere in the (mid-)western US you might want to visit, THEN fly back to MIA for a night or two of R&R before heading home!
MIA-Tampa/St Pete - Pensacola/Destin are all in FL and all great beach towns. From there, it’s a choice of how much “Americana” you’re interested in. Most Brits seem to like a day or two (or one night, at least) in New Orleans (NOLA). If Houston grabs your fancy, it’s a short hop from NOLA, and you can literally fly to anywhere from Houston!
Just a thought…