I misread the schedule. There is a flight on ANA for US $144 at 17:30. The reason I mention ANA in particular is because they are partners with Singapore Airlines.

You have lots of experts helping you - but just my small input. I think you really do need more time in Kyoto -- I'd try for 5 nights minimum (which would give you barely 4.5 days there). And I would cut back on Osaka for sure.

3. 13th-14th May 2019 Morning Bus to Mount Fuji and Hakone (2 nights)
4. 15th-16th Tokyo (2 nights) Day trip to Ashikaga Flower Park and Tochigo (optional or to be removed)
5. 17th May 2019 (1 night) Matsumoto for Alphine

I'm trying to figure out how this is going to work out?

On the 15th you leave Hakone for two nights in Tokyo. I suppose that means your day trip to Ashikaga FP is on the 16th (I don't know what you mean by Tochigo.

On the 17th you are going from Tokyo to Matsumoto. That is a short trip. You spend the night there. Then on the 18th you take the Alpine Route and end the day in Takayama?

OR

On the 17th you leave Tokyo, go on the Alpine Route, and spend the night in Matsumoto. Next day go to Takayama.

or something else?

Why are you going to to Tokyo and then backtracking to Mt. Fuji and Hakone? They are on the way from Osaka. Use rome2rio.com and hyperdia.com.

What are you planning to do in Osaka? I have been to Japan twice for a total of two months without visiting Osaka and I don't feel that I missed anything.

Why do you need to rest? You're only traveling from Singapore, on a daytime flight. In any case, Hakone is likely to be more restful than Tokyo, and you would save a hotel change.

That is about US$ 60 and I see that fare at klook but it is for Osaka to Nagoya. The Tokyo price is US$ 133 which would be about SG$ 180. That is the regular fare from Shin-Osaka. Your fare from Kansai Airport to Shin-Osaka would be about SG$ 37. The travel time by train from KIX to Tokyo would be a bit under 4 hours.

Instead of going to Tokyo you could just go to Odawara. It is on the way to Tokyo - about a half-hour less travel time. And it is a gateway to Fuji-Hakone National Park. From Odawara it is just 12 minutes to Hakone-Yumoto. There are a couple of travel passes that you could use for this part of your trip.

It sounds like you are planning to travel from Takayama to Kanazawa and then go to Shirakawago from there. But, Shirakawago is between Takayama and Kanazawa by bus.

There is plenty to do in Osaka for two days but the other places on your itinerary are more interesting and you are not giving them enough tine. Or, well, just a minimal amount of time, and it is not clear to me if you are considering travel time.

The partnership might mean that SQ will check you in for both flights, the one to KIX and then ANA flight to Tokyo Haneda. They might check your bags on through. You'd get to Haneda at 6:50PM and be in a hotel room in Shinagawa by 8:30 PM. The next morning you could get to Odawara in less than 30 minutes.

+1.

We've been to Japan probably 6 - 8 times in the last 5 years or so, usually for 2 - 3 weeks at a time. We've spent a grand total of 1 day in Osaka ... that was a few months ago and then only because we flew in to KIX fairly late in the day (7.30+ pm) and our next stop was Kanazawa, so we figured we might as well spend a day in Osaka. Osaka Castle (not nearly as good as Himeji), lunch and dinner in Dotonbori (certainly interesting to see - once - particularly at night when it's lit up etc. <and crowded> ) and a general bit of wandering around and we were done. Been there, done that, don't need to do it again. To me, Osaka, which is primarily a commercial city, has always seemed like a mini-Tokyo but without most of Tokyo's attractions. It's like visiting the U.S. and going to New York and then deciding the next place you should go is Pittsburgh or Cleveland or visiting the U.K., starting in London and then deciding the next place to go is Birmingham. Yes, you can, but why would you?

Kyoto, on the other hand, .... we've spent weeks there and never tire of going back.

mannequin_yeo, please confirm that the KLOOK fare from Osaka to Tokyo is around SGD 180 or give me a link to where the SGD 80 fare is available (to Tokyo, not Nagoya). It sounds too good to be true, but if it is then I would like to know more.

Could you give a narrative of the first three days? Include transportation, lodging, and sightseeing. For example, expand on the Fuji-Hakone part. You say you would take a morning bus to Fuji and spend a night then go to Hakone and spend a nightl. Ok,but what bus from where to where? Where will you stay the night and how will you get there from the bus stop/station. What will you do when you get there? Next you go to Hakone. How? When? Where?

I get the idea of your Matsumoto stop, but how will it work?

Here is a start, with two nights in Osaka at the beginning:
10th - Arrive KIX at 4:10 PM, take the train (JR rapid) to Osaka station, take the Westin Hotel shuttle bus and check in. Take a taxi to an okonomiyaki restaurant for dinner and back to the hotel.
11th - Visit Osaka Castle and the park around it in the morning. Head to Koshien Stadium around noon for the Tigers baseball game at 2PM. After the game, go to Spa World for a soak and have dinner somewhere, maybe at Osaka station, then walk back to the hotel if the shuttle has stopped running for the day.