It has to be New Zealand. It's somewhere that seems to be on everybody's wish-list yet many never get around to it and so meets your criteria of somewhere you may otherwise never go. I've never been myself and I guess I'm waiting to win a trip like you. It'll be summer when you're able to visit so it ticks that box too.
Nearest I've been is Australia and I loved it - such a huge, diverse country. It certainly isn't just sitting on beaches and hugging Koalas! I liked northern Queensland - I love the tropical heat, but it's not for everyone. There really is something interesting around every corner (OK, so the corners are VERY well spaced out, but still).
As a British ex-pat relocated to a small Greek island I must also suggest Greece, particularly the islands. I know you don't want to do Europe, but this really doesn't feel much like Europe in many ways - a little more detached and it's far enough from your German relatives too. You could also take in Istanbul while you're close as the other poster suggested. All the tales of the bad economy etc. in GReece really have almost zero effect on tourists so don't be put off by that. The best times would be May, June or early September. Choose a tiny island where you can kick back on a deserted beach with just a couple of little fish tavernas nearby and NO crowds, noise etc. and just do nothing for once.
Lastly, I'm surprised nobody has looked at your trip from an 'airliner-nut' point of view. If it were me, also having visited most of the places I want to see I'd be thinking "Hmmmm. how can I get on a TU-154, A380, 787, IL96 all on the same trip?". Get one of these round-the-world tickets where you can basically fly as many times as you like with a certain alliance. Might not be very relaxing for your wife but could be worth it.
Whatever you do - post a trip report here.
