I've done it. It's a nice ride. If you are riding a modern bike with plenty of gears it should be fine. I did it with a group of vintage cycle enthusiasts and we managed to ride most of it on old English three speeds: we had to walk more of the hills and one or two of the rougher sections. The section along Lake Pukaki is excellent on a fine day. The elephant rocks at Duntroon (the first photo) are a nice place to visit. Most of the climbs aren't too difficult. I'd definitely do it from Mt Cook or the alternative start at Tekapo to Oamaru and not in the reverse.
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Get a bicycle. You will not regret it if you live. ~Mark Twain, "Taming the Bicycle"
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