Nepal

The cheapest way in the world to spend weeks among the highest mountains on Earth. A tourist visa is available on arrival or online, at $30 for 15 days, $50 for 30 days or $125 for 90 days, and land borders expect US dollars in cash. The famous treks in the Annapurna and Everest regions run on teahouses, simple lodges where a bed is cheap and the money is made on meals of dal bhat, so walking for two weeks costs less than a few nights in many cities. Kathmandu's temple squares and lakeside Pokhara fill the rest of a month. Trekking permits add to the cost, and rules on hiring a licensed guide vary by region, so check them for your route before setting out.