Primary variables would be what season and what kind of mountaineering you want to focus on...secondary variables would be what languages you speak, how comfortable you are in the 3rd world, how much social life you want. And if you are doing some standard backpacking and sight seeing, everyone has some personal prejudice. For example my first big international solo trip was to Peru/Bolivia for 3 months. I went to see Machu Picchu so I added a few big climbs in the Cordillera Blanca. Pretty much everywhere around the world has some form of excellent climbing so the climbing itself doesn't necessarily need to be the decisive factor.
Having said all that, you can't go wrong with central California. It's prime time in Yosemite with the high mountains a short drive away for a reprieve from the heat. You can count on good weather with numerous options including glaciated stuff less than a day's drive north. With 6 months, you will have flexibility to get north to the Cascades, Tetons, Sierra and loads of less popular spots. If you've never been there, that would be my choice.
South Island would be a bit cold now, although it wouldn't be a bad option a few months later. Definitely world class mountaineering though I imagine it would be harder to find partners for any serious stuff compared to California. The territory is also a bit limited compared to the Pac coast, I don't think you would run out of stuff to do, but you might find it difficult to dodge crap weather.
Yangshuo is very nice, I've been there twice. Though you would be limited to sport climbing and there isn't much variety at that, all limestone and a lot of tufas. On the positive, it is a very social and international scene. Although I've heard there is some problems with access on some of the crags lately. Your costs will decrease if you like chinese food and know how to order it. Beyond Yanghsuo but still within China, there is little development for climbing.
If I were you and I wanted 'a heap of varied rock and mountain experience', I'd probably go to the Alps. It's amazing how often that place is overlooked. You definitely have to manage your costs but there is an ungodly amount of rock, it has all been climbed and it is very accessible and you'll find lots of climbers year round. Imagine all of Yosemite Valley and the entire Eastern Sierra accessible from your doorstep, then add rain and snow (a lot) - that's Chamonix. And with 6 months you would have unlimited possibilities for climbing or general touring...Spain, Scandinavia, Greece, Italy, Morocco...