Moving to Japan for two +months in Summer, need some help and advice please.

I’m moving to Japan to be near my two children (4y/o, and 2y/o).  They will be living in Yokohama with their Japanese mother for 8 months each year. We have a custody agreement and are no longer in a relationship.

I’d like to have fairly
easy access to Yokohama to see my children on weekends and I’d like to live in
the Tohoku region (I’m from New England and it is the part most like it plus I
want some distance between me and my ex and her family).  

I want to go hiking,
fishing (fresh/salt water), write poetry, read, visit or talk with Japanese
hunting clubs, and I’d like to join a Brazilian Jiu Jitsu school (I’m a brown
belt and have been training BJJ for ten years). 

My budget is between 1000
and 1300 per month and am thinking an AirBnB would be best.  I am fine
with Spartan accommodations as long as I have some privacy and wifi. 

I’ve been studying
Japanese for a year (Duolingo) but also lived with a Japanese speaker (who was
a Japanese language professor) and have children fluent in Japanese so my
language skills are bad but I can speak, read and understand some
Japanese.  I’d like to be somewhere where I can take Japanese language
classes to develop my language and somewhere that hasn't been impacted by over
tourism.

I’m a 46y/o male with a
remote job in publishing and I have a PhD in English literature and English
education. 

Any suggestions, help,
directions, cautions etc. are welcome.  I’m planning on moving from August
to the end of September (though I am flexible with this time frame). I am
trying to keep my stay under 90days to avoid needing a visa though I believe I
would qualify for a digital nomad visa if I applied.

Thank you very much!