Japan or Taiwan for two weeks

Hi!

I'm M28 from Europe and will soon be in Asia for the very first time in my life. I'll be there for six weeks and I'm looking for recommendations and help with a decision between Japan and Taiwan. I have a round trip from Europe to Singapore and I'll start and end my journey there. So my current itinerary looks like this:

09-12 October Singapore

12-20 October Malaysia

20 October-04 November Taiwan/Japan

04-19 November North Vietnam

19-20 November Singapore

I'm looking for a mix of cities with good food/museums/temples etc (not necessarily heavy into nightlife) and nature, especially for hiking and biking. I have a budget of about 2.8k for the whole trip left after the roundtrip flight to Asia and accomodations in Singapore.

I've heard mixed things about Taiwan, some told me that it's very interesting and incredibly good to get around while others said that it's not worth it. I've mostly heard good things about Japan but I'm not sure if two weeks (esp on my budget) will do it justice or if I should do it on a separate trip in a couple of years. But then again I've heard that it's comparatively cheap rn due to the weak Yen and that they plan to implement additional surcharges in the next years.

Thank you a lot for your recommendations in advance!