The best ryokan in Japan? :)

We are looking for a recommendation for a 1-night stay in a luxurious ryokan, up to 1000 USD per night. I already did some research and it seems there are options galore, so I'm looking for insights from people who actually experienced such a stay themselves :)

The requirements:

1. Private in-room open-air bath;
2. With a nice view;
3. Classic japanese decor, tatami;
4. 3-4h by train from Tokyo maximum;
5. Ideally, vegetarian-friendly.

We will be travelling in October. Thanks in advance! :)