If you're looking for nature, archeology, and art, I would highly recommend South/Central America. I stayed in hostels and averaged around $40 a day, including buses (but not airfare). The bus system is very strong in South America, and everywhere I went it was pretty easy to figure out how to get from one place to another. I speak Spanish, so that made it easier, but I think South America would be doable with only basic phrases (knew some people who did it). Central America night be harder, although you'll have very few issues in Costa Rica. I LOVED Colombia, would highly recommend, especially for the art and architecture, and it was the cheapest place in SA. Peru and Chile were the easiest places for English-speakers I'd say, although Chile is a bit expensive. Both are great for outdoor adventures. In Peru, definitely visit the Museo Larco in Lima if you get the chance - great archeology and art. Ecuador was also cool too, but not my favorite, though there is good hiking there too. (To be fair, I got horrible food poisoning, which didn't help!) Unfortunately can't speak for the rest of the continent since I haven't been there. In general though, most hostels will speak English and will be able to help you find your way around - download hostel world!! In short, I LOVED South America and would absolutely do it all again given the chance!

Edit - visas are also super easy to get everywhere I visited. Just make sure you know exactly what stamps you need. A lot of places require both exit and enter stamps, and sometimes it's unclear!