Over the past few years I've spent a total of five months travelling through or living in various remote corners of Africa. My advice would be to forget the Internet and all that is on it. Take a decent camera, learn photography. Take a local dictionary, learn the language. Take some art supplies, learn to paint. Take a guidebook and learn about the animals and plants. Get up for sunrise. Immerse yourself in the cult…
I found writing was a very nice activity when you're not connected. When I was travelling, I always carried a small notebook and a pen. It just started as random scribbles, notes and doodles about various things I was experiencing, but after a while my writing started having more substance. I realized it helped me understand cultures, people, languages etc. a lot better.
For example, I'd see/hear a word I couldn't understand, write it down in the original language and phonetically, then would ask various people how they'd explain the word (or expression). Translations are very rarely 1:1, so people have different ways of explaining the same thing, which I find very insightful. Writing these things down was a good way to organize and etch those things in my mind.