I should clarify a bit. Some dealers there will attempt to tack on a “location” fee because of a vehicle’s popularity, so in theory you could pay more than in other states.
What about buying an used car? It will be pretty dent and used after the trip anyways…
A motorcycle, 30 days with no real plans, and no road maps. The basic “Then Came Bronson” summer vacation. I’ve done a few and while some were more fun than others, all were well qualified as adventures.
Are you still thinking of flying to Alaska, then buying a car? Chefguy pointed out some issues you may run into, in post #17.
If you wanted to drive it all the way back to Sao Paulo, you’d still have to get across the Darien Gap, as Colibri mentioned in post #2.
You could fly to Alaska, rent a car, drive to somewhere in Central America, fly to South America, rent a car and drive home. Or rent a car in Sao Paulo, drive to Colombia, fly to somewhere in Central America, rent another car, drive to Alaska then fly home.
My credo is, the worse the experience is at the time, the better the story it will make afterwards.
Europe can make for a great solo adventure.
If you want to party, meet fellow travelers from around the world, see really cool stuff, and get laid then get a Eurail pass and hop on the first train leaving the station to somewhere you haven’t been. Stay youth hostels. Find a new person to spend the day with each morning at breakfast.
For a bit more difficulty you can hitch hike it. You meet a totally different set of people, and a lot more locals. Both ways make for great trips.
Most rental agencies in the US have serious restrictions as to where you can take their cars. I’m assuming that taking it out of the country (even across the Canada border) would be right out.
Dammit, Chefguy, would you stop pointing out all the mistakes in my posts? 
Okay, how about this- demian steals a car in Alaska, drives to Central America, hijacks a plane to South America, steals another car, drives to Tierra Del Fuego, commandeers a ship and sails back to Sao Paulo? That would be quite an adventure. I suppose there’s something wrong with that plan? 
This is true. I once rented a car in Detroit and drove it across the Port Huron/Sarnia boarder. The customs officer in Canada informed me it was against the law, but let me go anyway. I was visiting my parents for one night only and was returning to Detroit for a training course the next day.
"The test of an adventure is that when you’re in the middle of it, you say to yourself, ‘Oh, now I’ve got myself into an awful mess; I wish I were sitting quietly at home.’ And the sign that something’s wrong with you is when you sit quietly at home wishing you were out having lots of adventure."
–Thornton Wilder, The Matchmaker
Yeah, I rented a car recently while mine was in the shop. The restrictions were Washington and Oregon ONLY.
You could try driving from Key West, Florida to Deadhorse, Alaska. Lots of scenic areas, plenty of places to stop along the way and plenty of routes to take. Wanna drive through hillbilly towns in West Virginia (country roads, take me home, etc.)? Wanna go by way of Texas? Maybe drive to Niagara Falls and then go across Canada? You can.
Appalachia, as a region, is very safe. One of the safest parts of the country, and also one of the most heavily armed places too. People are polite.
Reminds me of renting cars in Hawaii. On Maui, a common restriction is, or at least used to be, don’t drive to the top of Haleakala (where everyone went to watch the sunrise), and on the Big Island it was don’t take the Saddle Road across the middle of the island. But we ignored those restrictions and saw lots of other rental cars doing the same. There were perfectly good roads, but our guess was the car-rental agencies didn’t want to have to go all the way out in the boonies in the event of a breakdown.
Because they were moving to DC I did the Canadian MLB tour & went to see the Expos & Blue Jays. Enterprise didn’t have any issue with it (other than some add’l paperwork). I made sure that they were aware of the international travel so I wouldn’t have any issue in case something went wrong (breakdown or accident). I don’t know if they’ve changed their policies since, though.