This sounds alot like the "Monk and the Riddle" philosophy. Is this what you're getting at?

Where would you live? In your own house? On your own island? Or somehow work in a company that lets you spend your free time working on an open source project?

Possibly in my own house on my own island ;P

But I'd certainly go for maximum independence so going to work for a company if I don't have to (which presumably I won't have to if I sell a startup) is out of the question. I want to be able to pursue crazy projects that might or might not turn out to give results.

Oh, and I'd crank up on my knowledge of theoretical CS too.

Talk to your parents.

It's amazing what the response to

"I just recently graduated. Instead of going to Europe to get drunk for a year, I'd like to go home for a year and write software for my startup."

can be.