These suggestions are almost all absolutely terrible. Sure, Botswana and Zambia are amazing. Will you have any fun there at all on 4K, on your own, and not speaking any of the languages? I'm sorry, do you speak Swahili? Afrikaans? No? Then what the hell are you going to do? The "safe" places for a Westerner will go through your budget very, very quickly. Not to mention the 2K in airfare to get there.
Other suggestions like Ireland are also terrible. The airfare costs a great deal, and Ireland (well, most of Europe) is outrageously expensive. Have you checked how the US currency is doing against the Euro recently? Not too hot. Groceries in Ireland will come as a huge surprise. Figure on one and a half to two times as much as anything costs here in the US, at a minimum. Petrol (that's gas for you Americans) will cost a small fortune. Hostels are alright, but you're still going to be spending a premium. Your 4K will not last long at all.
Chile and go skiing? Seriously?? I'm sorry, but the last time I checked 4K doesn't work for $1,200 in airfare, $75-$100 per day for lift tickets, $30-$50 per day for resort food, and the large expense of staying at or near a resort.
To stretch your 4K and have a good time, you need to go somewhere economical, and somewhere that English is a primary language. This limits you to North America, Australia, New Zealand, and parts of Europe. Don't even get me started on how expensive Australia is. If you want more than a one week trip, rule this out on a 4K budget. The same goes for New Zealand and Europe.
Well now, we are left with North America. This is not a problem. North America is a vast and VERY varied place. Have you fully explored even our own country? Have you seen the Southwest, run through the saguaros, explored forgotten canyons, and ran with the wild horses? Have you been above treeline in the High Sierra, at a crystal clear mountain lake eating the trout you just caught for dinner? Have you heard the elk bugling in an alpine meadow in Wyoming? What about the charm of a small Southern town? The relaxed and earthy customs of rural Oregon?
If the US bores you, visit Canada. Montreal will feel like a foreign country, and has more clubs than you could visit. British Columbia, specifically the Sea to Sky corridor, is a wonderful place. It stays light until 10:00 PM during the summer. Go earn your turns up toward Whistler on a glacier.
If you stay in North America you can explore our wonderful country and Canada. You will be familiar with the languages and customs. Your money will last for a few months if you're frugal. Go see what makes America great.