A few words concerning cars.......
Hello Rearden86,
Your English is very, very good, by the way.
It seems as though you and your wife are planning a long and enjoyable trip. I hope it goes well for you.
Concerning renting a convertible: Don't get me wrong--I love convertibles and I am the proud owner of a 1966 Chevy Impala convertible. The time of year (late summer) and your general route (across the Gulf Coast, all of Texas, NM, AZ, and NV) may combine to make travel in an open car close to unbearable. My neighbor is from Norway, and he suffers in the North Carolina summers, which aren't nearly as hot as in New Orleans, Houston, etc. Most convertibles have air conditioning, so one could readily choose when to "drop the top", but I wonder just how often that might be. That, in turn, leads to "why bother, and why incur the additional expense?".Aside from being in the direct sunlight, the buffeting from the (very hot) wind while on the open highway can exhaust you very quickly. Simply said, a 400 mile day in an open car during summer can be far more fatiguing than in an enclosed air-conditioned car.
But, you might consider a plan to turn in a conventional car in LA and rent the convertible for the Pacific Coast Highway. On my one trip down the PCH, it seemed that every 3rd or 4th vehicle was a rental Chrysler Sebring convertible.
Concerning "things to do" related to cars and glimpses of Americana, you'll be traveling during racing season and you are likely to be within a short drive of a local stock car racetrack or dragstrip on most any Friday or Saturday night. A good national listing on a state-by-state basis can be found at speedwaysonline dot com. I expect there would be quite a number of local rodeos going on during the weekends, too. A dirt-track race on a Friday night followed by a rodeo on Saturday evening would be a fun, if dusty, way to see some sights few Europeans see.
Have fun with the planning and the RoadTrip!
Foy