It makes absolutely no economic sense to land on an oil rig. In fact, it makes no sense whatsoever. They cost half to three quarters of a million dollars a day to rent. Furthermore, an oil rig is covered with a giant drill tower, various cranes, housing and offices, drilling machinery and oil processing equipment, and so on. The only flat spot on an oil rig where you could possibly land would be the helipad, which is far too small and fragile for the stage to land on. You can't get rid of the cranes, because you need them to lower the stage onto whatever barge you're going to use to ferry the stage back to land.
On the other hand, there's lots of big empty swaths of land at Kennedy spaceport. There's lots of big empty swaths of land near the proposed Texas site. Just put down on a landing pad right at the spaceport.