Hitchhiking is not part of the local culture (unless you're a Monk). And in Nay Pyi Taw, with an increase in traffic, people are even less likely to stop. I picked up a couple a few nights ago who had been waiting for ages and almost missed their train.

As for things to see, it depends on what you're interested in. There are the Gem museum, national museum, defence services museum. The zoo, planetarium, national landmark garden, herbal garden and water fountain park. Plus the Uppātasanti Pagoda and "little Bagan". You can even visit parliament, although it'll take +/-5 days to get security clearance. Of course, most tourist come here just to see the 20-lane highway.

As for taxis, there are 2 problems. 1) they are more expensive than other cities. For example, hotel zone to the pagoda will be around 10,000 Kyat. 2) Taxis don't ply the roads like other cities. So if you take a taxi from A-to-B and let him leave, you will struggle finding a taxi to get from B-to-A. There is a taxi rank outside Junction and a moto-taxi rank outside Capital. Other than that, hotels offer taxi services (though it's even more expensive)

Don't get caught up in the superficialities of the "dead city". Nay Pyi Taw is certainly not as busy as a typical SE Asian city, but rumours of its death have been greatly exaggerated. A backpacker staying in the hotel zone, maybe visiting Junction Mall at noon on a Tuesday will come to the false conclusion that there is no life here. But go to Myoma or Thabyegone market for dinner where you may have to search for a free table. Don't just travel on the Yaza-Thingaha or Yaza Htarni road (20-lane highway) but go 1 street in to see there are buildings and people and life.

I've done some hiking on the Kumano trails of the Kii Peninsula. There are some great long-distance hiking trails there, which pass entirely through nature and villages (there are no cities, or even big towns, in the region at all), and it's possible to wild camp. The trails aren't of the sort of length that you describe, though you could try combining that with something else if you wanted.

The interior of Shikoku is rugged, mountainous, and very sparsely populated. With a bit of work, I'm sure you could put together your own Shikoku trail that took in some great mountain temples, and stayed away from the island's main roads and towns. Many of the more remote temples on the island are part of a sort of "add-on" to the 88 temple pilgrimage that exists, so you could look to that for a starter.

I don't know what the Tokai Shizen Hodo is, but I'm very aware of Western Japan (and have done numerous day-hikes all over the Kansai region). It's very difficult to stay way from populated areas on the way to Osaka.

I personally really enjoy hiking the countryside in Kansai, but don't know if that would be to your tastes. The north of Japan (ie. Tohoku and Hokkaido) is more wild than the rest of the country, but I have no personal experience, and don't know if there are good long-distance hiking trails there.

Yes, we chose Montana and loved it. We had time so we chose to take a shuttle to Hidroelectrica and walk to Aguas Calientes (2.5-3 hours scenic walk). We stayed overnight in AC. The next morning we first visited the site and then hiked Montana. We then stayed in AC for another night and walked back to Hidroelectrica and took a shuttle back. But you really need 3 days for that.

Most people take a train and I suggest taking the train from Ollantaytambo (more departures than from Cusco). So late afternoon take a train to AC, stay overnight and in the morning visit MP and hike the mountain of your choice. After MP take a train back to Ollantaytambo.

The MP tickets have changed again this year though. Now the ticket also says from what time you can enter the site. For example for Montana you can choose from 6 or 7 am to enter the site and 7 to 8 to hike the mountain. Or from 8 am to enter the site and 10 to 11 to hike the mountain.

It also depends on how long you have. You will want at least 5 days for Cusco, the Sacred Valley and MP (if you take the train). MP is of course great but there are many other amazing sites in the area. If you have more time and like to hike you can also consider a trek.

Osaka definitely isn't a major attraction. Just a smaller, blander, less interesting version of Tokyo.

Kyoto will be mobbed during golden week. I'd try to do it before the holiday if possible.

Mt Fuji is closed for hiking at this time of year. Seeing it from Tokyo or the train line south of the mountain is not difficult on a clear day. If you want to explore a scenic area like 5 lakes or Hakone it will be mobbed during golden week. I would avoid if possible.

Some thoughts:

Fly in to Taipei then train to Chiayi for two nights with the intervening day riding the forest railway>

Two nights in Chiayi is two too many. OK, that's a little harsh. Chiayi Park is an okay place to kill some time, and there's a decent night market on Wenhua Road. But Chiayi shouldn't be more than a place to spend the night before catching the Forest Railway train the following morning on the way to Alishan (with Fenqihu and Ruili making great stopovers).

Train from Chiayi to Fuyuan (east coast) and again two nights with day visiting the forest>

There are no direct trains between the two stations, so at least one change of train would be required. Taiwan has a number of forest recreation areas - what attracted to you to Fuyuan, one of the lesser-known ones?

Train from Fuyuan to Hualien with three nights one day spent going to Taroko Gorge>

Three nights is a long time to stay in Hualien. You might want to consider using one of those nights to stay in Taroko Gorge itself.

Train from Hualien to Ruifang with three nights there and daily side trips>

There are a lot more convenient places to base yourself in than Ruifang, which basically serves as a transfer point for travelers going to Jiufen from Taipei. In fact, it would be much better to stay in Taipei and visit Jiufen, Keelung, the Pingxi Branch Rail Line and so on as day trips from the capital.

Seeing as it will be your "first extended experience" in Asia, why not spend time in Tainan, Taiwan's historical capital, home to a number of temples and other historic buildings, not to mention having some of the best street food in the country? Lukang is another historical town worth visiting. And if you're up for a challenge, renting a car and exploring Taiwan's Central Mountain range and the stunning east coast (especially the Suhua Highway) can be a rewarding experience, though driving on the narrow roads and dealing with Taiwanese drivers might not be everyone's cuppa.

being Australian we're unaccustomed to the cold.

The destinations you have listed are not in the Arctic. If you've spent time in Canberra, Alice Springs, or even Melbourne during the winter you will cope. Bring layers -- you need may need all of them when outdoors but you will soon want to be rid of them when indoors. Gloves may be a good idea, but then you have to keep track of them. Pockets can be a practical subsittute.

Five nights in Lyon will be excellent. Good food, friendly locals, and lower prices than in Paris.

Basel is lovely, and it's my second-favourite city in CH. There is much to see in and around the city, and in its suburbs in France and Germany, including Christmas markets and decorations and old buildings and art and design museums. And the Rhine! Plus you've got to admire a population that is capable in two or three varieties of German plus French and English. There will be plenty of colour to draw your attention away from the grey skies. But Basel doesn't offer any mountain views that people associate with CH. Perhaps look at moving to Luzern for two nights for the full-on winter experience with mountain views.

You will need to backtrack to Zürich for the train to Innsbruck, however. And it may be that the mountain views between Zürich and Innsbruck will suffice.

I agree with many here.

Hiroshima is not must see on a short trip. Even if you still want to see it, 2 nights is excessive. It can be done as a tight day trip from Kyoto or a very leisurely 1 night.

Kanazawa deserves 2 nights, but as everyone says, it is not in the alps, not near mountains. It's a mini Kyoto with some other cultural attractions.

Matsumoto to Tokyo shouldnt involve a detour to Nagano or Nagoya, as they are directly linked by a beautiful and cheap railway.

I always like Hakone as a flexible day trip rather than a fixed night.

If you are committed to starting in Kyoto, try to fly into KIX. If you have already purchased flights to NRT or find them to be $150-200 cheaper than an open jaw into KIX and out of TYO, then consider looking at cheap flights to bridge the distance. Yes you CAN take a train from NRT to Kyoto on your first night but it isnt cheap or pleasant.