I'd go through Patagonia down to Ushuaia and take a cruise to Antarctica. It's feasible with $10,000 if any form of luxury is avoided. I was in Peru for 2 months last year when I injured myself trying to be the first in my group to descend from Mt. Salkantay (very stupid). I had planned on going to Patagonia shortly afterward, but didn't want to go without being capable of doing everything I wanted to do so I left earlier than planned. I had lost 2 weeks of time slotted for this anyway waiting for replacement debit/credit cards to be mailed to me from the states. Huge regret, but it's not an adventure if everything goes according to plan. I need to go back and finish it. Second on the list would be going around Africa with a climax of summiting Mt. Kilimanjaro.