You know you are going to cry, so carefully plan it for effect. Anonymous is good. Unnoticed is pathetic.
You're onto something with the rental car idea, but you might want to rent a really expensive car and drive it to some touristy spot with a great view. As evening falls, and the lights of the city or bridge or whatever start to glow, slump over the wheel and let it all out. The wide-brim hat suggestion goes well with the fine outfit you are wearing. It also maintains anonymity and heightens mystery.
Not only will you feel much better, but you will have lifted the spirits of all who notice and wonder how that person with everything can be so unhappy. They'll think, "I may not be wealthy, but at least I'm not like that person."
And the the odds of finding your act in a novel at some later date are much improved.