... a place to hide from all the people trying to get my money. A name change. Unlisted phone number.
I would pick up the check wearing a ski mask, coveralls, gloves and sunglasses with nobody I know around.
With a $360 Million jackpot, you'd probably take home around $100 million after taxes.
Make some investments with a good broker. Get some nice real estate to use as rental properties.
Buy a row of average size houses to let 4 of my friends live there if they want, but I keep the deed. They can stay as long as they want for free though. And have 1 main big house with a pool, bar, entertainment room, etc..
Bugatti Veyron, Lamborghini Murcielago, Ferrari F430 Spyder, A big van or SUV (not a flashy one) with a part time driver to haul our drunk asses around town safely on the weekends, and a few Toyota Priuses as grocery getters for me and friends.
And I would never get married.