You could do with finding out if she means travelling independently round some exotic or culturally different location or a long overnight hiking route. Very different!
2 weeks isn’t long but there are some amazing multiday hikes in the USA and Canada which are very well signed and offer big landscapes or big mountains. The Pacific Crest and Appalachian are well known but every National Park and most National Forests will have something. Into the Grand Canyon for 6 nights? Other canyonlands in Utah and Arizona, High Sierras in California are all very easy to organise yourself. I friend did bits of the High Sierra Trail for 6 days and didn’t see anther person for 2 days in the middle. Versus friends who did the camino de Compostela de Santiago where you see pretty much the same people at the hostels each night. Depends if you are social or not which one you will enjoy!
Whereas cheap and cheerful backpacking, if you have never left Europe, I would highly recommend. South America (Peru / Ecuador particularly) for very cheap transport, accommodation and food. Adding in Patagonia or Brazil gets more expensive (mostly transport) and would need more than 2 weeks. Costa Rica is very well organised in terms of public transport, because they’ve had lots of subsidy, but it is very Americanised in particular the beach resorts. I love South Africa and East Africa. To really get the best of it, you have to pay for some bits like safari (though you can self drive in SA) but you can do a lot with public transport and hostelling. The classic south east Asia trail can be a bit 18-30’s or family oriented beach resorts with not much in between. However, if you head slightly off the beaten trail you could have a really interesting experience (possibly Laos / Cambodia although they too have become popular; islands away from Bali in Indonesia; Phillipines for scuba diving). The classic (for people 20+ rather than pre-Uni teens) is to head to Australia and hire a campervan. We did Melbourne to Brisbane in 2 weeks because of cheap flights – I would recommend Melbourne to Sydney or Adelaide to Melbourne over 2 weeks. If you want more ideas, can read lots on line these days from Lonely Planet, Rough Guides and Brandt and Fodors and use the Lonely Planet forum Thorntree. Personally if I had never done anything like that but only had 2 weeks, for cost I would go for south-east Asia (Indonesia probably) and for experience I would go for Africa (either Uganda/Rwanda to see the chimpanzees and gorillas if you can afford it, or the Western Cape because it is really easy to do and has so much outdoorsy stuff to offer as well as the human history).