There are stretches of beaches that you can drive on. The 'Lost Highway' is where I took the pic in my avatar. About 30 miles where it's relatively un-populated. Probably some topless-ness you don't want to see. It's not completely clean though, and I did see get some tar on the truck to deal with after.
I was going to ask, where is the Lost Highway. Sounds similar to possibly the Padre Island National Seashore. From what I understand, there are 60-70 miles of natural beach area that you can pretty much drive around at any speed you care to. I have that place on my list to visit. The only problem is it really is a natural area with no facilities. So my wife wants to know how she is expected to go to the restroom when we camp there.